The Red Devils were heavily linked with the 23-year-old in the summer transfer window, amid speculation surrounding Harry Maguire's future.
The England international attracted interest from West Ham United, but he ultimately remained at Old Trafford following the transfer deadline.
Although Maguire has since worked his way back into Erik ten Hag's plans, Man United are still on the lookout for a new centre-back, with Raphael Varane and Jonny Evans out of contract at the end of the season.
With the Red Devils searching for defensive reinforcements, Todibo continues to be regarded as a potential transfer target.
There has been a suggestion that new Man United investor Sir Jim Ratcliffe could facilitate a move due to his links with Nice.
The billionaire has been the primary owner of Nice since acquiring the club in the summer of 2019, but it is currently unclear whether he would allow Man United to buy a player from the Ligue 1 side.
While Ratcliffe's position may be unknown, Nice's sporting director has made it clear that Todibo will not be allowed to leave the club this month.
Speaking to Get Football France, Ghisolfi said: "We want to have stability, and stability is keeping your best players. Jean-Clair and Khephren Thuram are definitely that. We absolutely want to keep them."
Todibo is also believed to be keen to stay until at least the summer, as he looks to secure his place in the France squad for Euro 2024.
Having made 14 league appearances this season, the 24-year-old is regarded as a key member of Francesco Farioli's, and he does not want to risk losing regular game time by leaving the club in January.
Although he is unlikely to depart this month, his future could draw significant speculation in the summer transfer window.
In addition to Man United, Todibo is being tracked by German champions Bayern Munich, while there has also been interest from Chelsea.
With Todibo under contract until June 2027, it could take a fee in the region of £52m to prise him away from the French Riviera in the summer window.