The 20-year-old, who joined the Spanish outfit from Lens in 2012, was arguably his side's star player during his first season in La Liga.
Such performances have drawn interest from a host of European clubs, with Sevilla hardly in the position to turn down a sizeable bid for a player they signed for little over £2m last summer.
Here, Sports Mole picks out five possible destinations for the France Under-20 international.
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With United seemingly set to miss out on Barcelona midfielder Thiago Alcantara, the Premier League champions' attention could quickly switch to Kondogbia, who is believed to be keen on a move to the Premier League.
It is some time since United invested in their central midfield and it does not take a genius to realise that is the area that is in dire need of strengthening ahead of the start of the league campaign in August.
Not only does Kondogbia boast the physical assets to perform in the Premier League - standing at 6'3" - the youngster is also adept on the ball and has a keen eye for a pass.
United will certainly face competition for the Frenchman this summer and boss David Moyes must move quickly if he is to make the midfielder a key part of his squad for the new season.
Madrid have long been linked with a move for the Frenchman, but a bid has been thrown into doubt with the recent signing of Real Sociedad midfielder Asier Illarramendi.
The capital outfit have also acquired Isco from Malaga this summer, but there is no question that the powers-that-be would be prepared to open their chequebook once more if Kondogbia became available for the correct price.
Sami Khedira's future with Madrid has been thrown into question in recent months, which could open the door for Kondogbia to provide some bite and muscle to the middle of their midfield.
Reports have suggested that Kondogbia is settled in Spain, which would make Madrid a viable option should the promise of regular football be attained.
If recent reports are to be believed, Arsenal have emerged as the favourites to sign the powerful midfielder this summer.
There is no question that the youngster has the footballing ability to operate at the club and also possesses the physical attributes to compete against the more powerful teams in the English league.
It has long been suggested that the Gunners are prepared to spend big this summer, but their best piece of business could yet be another emerging French talent.
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Michael Essien, who spent last season on loan at Real Madrid under Mourinho, will return to Stamford Bridge this summer, but he is not the same player who graced the Premier League during his first spell with the club.
There are also question marks over the long-term future of John Obi Mikel, who has been strongly linked with a number of Turkish outfits in recent weeks, while young Spaniard Oriol Romeu has joined Valencia on loan.
Mourinho will certainly be aware of Kondogbia's talent having come up against the Sevilla midfielder last season, which could prove to be decisive when attempting to convince the Frenchman to join the Blues.
Should Spurs keep hold of Gareth Bale this summer, in addition to signing two new strikers, they will be strong challengers for the top four next season.
Spurs would surely be able to guarantee Kondogbia first-team football, which would hand the London outfit a large bargaining tool when meeting with his representatives.
Having missed out on the Champions League once again last season, Villas-Boas could see the powerful Frenchman as the ideal player to add something different to his midfield.