After brushing aside West Ham United in their opener, Red Devils boss Jose Mourinho has supporters dreaming of an end to the club's five-season wait for top-flight silverware, while the Swans are simply hoping to avoid another relegation scare.
Placed among the favourites to drop down to the Championship for large parts of the 2016-17 campaign, Paul Clement deserves huge praise for not just steadying the ship but helping to lift his side out of the dropzone.
The Swans may never have finished below 12th place in their previous five years in the Premier League, but ending in 15th was an impressive return and leaves them in a good position to push on for a safer season ahead.
That is the hope, at least, as Clement has had to contend with losing prized asset Gylfi Sigurdsson, who finally completed his £45m switch to Everton this week after months of speculation and drawn-out negotiations.
City chiefs will no doubt welcome the cash windfall for a player re-signed from Tottenham Hotspur three years ago in a straight swap deal with Ben Davies, though time is fast ticking down to bring in an adequate replacement - or replacements, as it will likely transpire.
Sigurdsson played a direct part in 22 goals last time out in a season that ultimately ended on a high for the Welsh outfit, creating more chances from set-piece plays than any other player in the top flight.
Stuart Armstrong, Nacer Chadli and Joe Allen are the three names being whispered around the Liberty Stadium, with Clement needing to move fast to add some more creativity to the middle of the park if he is to avoid seeing his side embroiled in another relegation scrap.
Swansea finished the previous season with 13 points from their final five games; form they maintained on the opening weekend of this campaign thanks to a rather fortuitous point away to Southampton, making it six without defeat now - their best run since January 2013.
With United and Tottenham to come in two of their next four outings, keeping this run of momentum going may prove tough, but the fixture list has otherwise been kind to the Swans and they have a real chance to get some early-season points on the board.
Recent form in Premier League: D
For all of United's struggles in the Premier League last season, eventually finishing in sixth place and some 24 points adrift of champions Chelsea, their away form remained among the best in the country.
In fact, only two other sides - Chelsea and Manchester City - picked up more points on their travels in 2016-17, winning 10 and drawing five of their 19 matches in all.
It was at home where they proved far more charitable to opposition sides, drawing a total of 10 matches at Old Trafford and seeing any hopes of challenging for the title completely fade away before the business end of the season arrived.
Playing West Ham at home in their first outing of 2017-18, a side expected to finish somewhere in mid-table this term, provided the Red Devils with a good chance to see exactly how far they have come since strengthening during the summer months.
It was a test they passed with flying colours, racking up four goals in what was arguably their best Prem display since Mourinho took charge a little over a year ago, with league debutants Nemanja Matic and Romelu Lukaku both impressing.
There was a ruthless nature to United's performance that was lacking so often last time around, as Mourinho refused to put the handbrake on and was rewarded with a couple of late strikes to lift his side to the top of the table on goal difference.
Club-record signing Lukaku netted two of the four goals and is now on course to become just the fifth United player to score in his first two Premier League outings for the club, joining a list that includes Zlatan Ibrahimovic, Anthony Martial, Federico Macheda and Louis Saha.
On the basis of their first league match, the Red Devils will be serious contenders for the title this time around and, judging by their upcoming fixtures - just Everton to face among the heavyweight sides before mid-October - they could lay down a real marker to their rivals.
Recent form in Premier League: W
Recent form (all competitions): LW
Swansea are still without star striker Fernando Llorente as he continues to recover from a fractured arm suffered while cycling on holiday during the off-season, keeping him out for the opening fortnight of the campaign.
Ki Sung-Yeung and Nathan Dyer are the other notable absentees this weekend, but a debut could be handed to Roque Mesa following his arrival from Las Palmas during the summer - a player boasting the second-highest pass-completion rate in La Liga last time out.
Clement may opt to stick with the same XI that held Southampton to a goalless draw at St Mary's last weekend, however, using Chelsea loanee Tammy Abraham through the middle in a 4-3-3 formation.
There is some better news elsewhere, though, as Victor Lindelof should be fit enough to feature in the matchday squad, but the Red Devils are unlikely to tinker with a winning formula.
Paul Pogba impressed when given licence to roam into more advanced positions against West Ham, thanks in large to the defensive workload of new midfield partner Matic, meaning that recently-appointed captain Michael Carrick could again miss out on the 18-man selection entirely.
Swansea City possible starting lineup:
Fabianski; Naughton, Fernandez, Mawson, Olsson; Carroll, Britton, Fer; Ayew, Abraham, Routledge
Manchester United possible starting lineup:
De Gea; Valencia, Jones, Bailly, Blind; Matic, Pogba; Mata, Mkhitaryan, Rashford; Lukaku
Head To Head
Man United have won two of their last three Premier League meetings with Swansea, drawing the other, having lost the previous three by the same 2-1 scoreline.
The Swans have failed to keep a clean sheet in this fixture in 12 Prem attempts, although they did nick a point at Old Trafford in the most recent of those encounters through a late Sigurdsson goal.
Two quick-fire goals in August 2015 helped City to a 2-1 win over the Red Devils, but they have been less successful in the three clashes since then.
We say: Swansea City 0-2 Manchester United
After ending their mini hoodoo against the Welsh club, United head into the match as strong favourites to maintain their perfect record to the new Premier League campaign. Mourinho saw his side comfortably see off West Ham last weekend and, with his summer recruits settling in nicely, this offers another chance to get some points on the board early on.