The 27-year-old has rarely been far from the headlines since rejoining the Red Devils in a world-record deal four years ago, and with his contract currently due to expire next summer there has been speculation that United could look to cash in on him.
Pogba has been limited to only eight appearances during an injury-plagued 2019-20 season, but manager Ole Gunnar Solskjaer has repeatedly stated his intent to keep him at Old Trafford.
Recent reports have suggested that they could be interested in a swap deal for the World Cup winner, though, with few clubs likely to be able to afford his transfer fee and wages in the post-coronavirus market.
Adrien Rabiot (Juventus)
Rabiot has been increasingly linked to United over the past week, with reports claiming that the 20-time English champions have already made contact with his representatives.
The Frenchman was one of the hottest properties in Europe last summer when he was available on a free transfer, but things have not quite gone to plan for him since Juventus won the race for his signature.
Rabiot has made only 11 Serie A appearances for the Italian champions and is thought to be open to an exit in search of more regular first-team football.
The 25-year-old is valued at significantly less than his compatriot, though, so Juventus would likely still need to stump up a significant amount of cash even if they do use Rabiot as a makeweight.
Federico Valverde (Real Madrid)
Given the freedom to choose any Real Madrid player they want, Manchester United may well pick Federico Valverde.
The 21-year-old has emerged as one of Zinedine Zidane's most important players this season, making 32 appearances across all competitions while scoring twice and creating four goals more.
Pogba would still be regarded as more valuable than the Uruguayan, although Valverde's age and potential would take a large chunk off United's asking price for the Frenchman.
However, the biggest obstacle to such a swap is Madrid's reluctance to lose Valverde, whom the 13-time European champions view as one of the foundation blocks for their next generation.
Aaron Ramsey (Juventus)
Another Juventus player who has failed to really make his mark in Turin since joining on a free transfer last summer, Aaron Ramsey has been tipped for a quick return to the Premier League.
The former Arsenal stalwart has made only nine Serie A starts and 24 appearances in total this season, although in that time he has still managed to score four goals and create another.
Reports have suggested that Juve would be open to including Ramsey as a makeweight in any deal, having not paid a transfer fee to take him from Arsenal last year.
The Welshman's experience of the Premier League is also a bonus for United, although at 29 - 30 in December - he may be a little outside the target age bracket for Solskjaer.
Marco Verratti (PSG)
Verratti has regularly been linked with a move to Manchester United down the years, and at 27 years old he still has plenty of time in him at the top level.
The Italian has once again been a regular member of the PSG first team this season, contributing six assists in 33 appearances across all competitions while continuing to act as a midfield destroyer for the French champions.
PSG are unlikely to force Pogba into having the same levels of defensive discipline as Verratti, though, and would therefore not view this as a straight swap with like-for-like players.
Verratti is also still a highly-valued player at the Parc des Princes and only signed a new long-term contract with the club in October.
Miralem Pjanic (Juventus)
Like one or two others on this list, age could prove to be a deterring factor in accepting Miralem Pjanic in any swap deal, although there is no doubting the 30-year-old's enduring quality.
The Bosnian has made 32 appearances across all competitions this season and acts as the conductor for those in front of him to weave their magic - something United are in the market for this summer.
However, the fact that Pjanic does not fit in with Solskjaer's desired target of young British players is not the only potential stumbling block, with Spanish giants Barcelona also understood to be interested.
The playmaker reportedly views Camp Nou as his preferred destination should he leave Turin and could therefore be opposed to his inclusion in any deal for Pogba.
Toni Kroos (Real Madrid)
Manchester United have come within a whisker of signing Toni Kroos in the past and have held a very long-standing interest in the Germany international.
Even at 30 years old he shows no sign of slowing down, having scored five goals and assisted nine more in 33 appearances for Real Madrid across all competitions.
A move to Old Trafford has clearly appealed to Kroos before and may do so again this summer, while Madrid may feel as though they have got the best years out of the World Cup winner and could significantly lower Pogba's price with his inclusion.
Kroos's value was only increased when Madrid tied him down to a new long-term contract last year, with the midfielder committing himself to the Bernabeu until 2023.
Douglas Costa (Juventus)
Another player who has repeatedly been linked with a move to Old Trafford throughout the years, Douglas Costa would by no means be a straight swap but could be a satisfactory one for all parties.
The 29-year-old is considered disposable by Juventus having made only six Serie A starts all season, while United are in the market for a new winger and have long been interested in Costa.
Borussia Dortmund's Jadon Sancho is their top target in that area of the field, but he is expected to cost in excess of £100m whereas they are likely to get Costa and cash if he is included in a deal for Pogba, freeing up money to bring in someone like Jack Grealish.
For Costa it would also be a chance to get more regular first-team football and revive a career which has somewhat stagnated despite his obvious talent.
James Rodriguez (Real Madrid)
James Rodriguez's star has plummeted dramatically since winning the World Cup Golden Ball in 2014, when he was also linked with a move to United before eventually joining Real Madrid instead.
The Colombian spent the 2017-18 and 2018-19 campaigns on a two-year loan at Bayern Munich, but they decided against making the deal permanent and he has subsequently returned to the Bernabeu this season.
Rodriguez is yet to impress Zidane enough to work his way into the first team on a regular basis, though, making only four La Liga starts and 13 appearances across all competitions.
United are one of a number of Premier League clubs to have been linked with him, and at 28 he still has time to reignite his career, but high-profile players on hefty salaries who are seemingly on their way down are exactly the type of signings the Red Devils are hoping to get away from at the moment.
Paulo Dybala (Juventus)
Dybala was on the brink of signing for United last summer only for Juventus to decide against selling the Argentine, who at one point seemed destined to come to the Premier League.
The 26-year-old is probably the player closest to Pogba in terms of value in this list and may well be a big enough draw to warrant a straight swap, while also providing United with another star name to replace the one that would be leaving.
However, Dybala has worked his way back into favour at the Allianz Stadium this season and it is understood that he is now much closer to signing a new contract than he is to being sold - a sharp U-turn from almost 12 months ago.
Dybala has scored 13 goals and created 12 more in 34 appearances across all competitions in 2019-20 and is keen to remain in Turin, just as he was last year despite Juve's attempts to offload him.
Gareth Bale (Real Madrid)
Bale would also fall into the 'James Rodriguez' category now, although at his best the Welshman remains one of the world's most effective players and United have been linked with him for the best part of a decade.
A mixture of injuries, form and apparent indifference at playing for Madrid has threatened to overshadow his time at the club, where he has won four Champions League titles and scored 105 goals since becoming the world's most expensive player in 2013.
In terms of star power few can match Bale and the prospect of finally bringing him to Old Trafford after years of trying could prove to be tempting for Ed Woodward.
However, the 30-year-old's wages are a sticking point and the fact that United's main competition for his signature would be from the MLS, Chinese Super League or Newcastle United could be a warning sign about the direction his career is heading.