While there is no clarity yet over whether Real Madrid would be willing to part ways with the 26-year-old, there is a growing belief that his position at the club could come under pressure in the coming weeks.
Real Madrid are in the process of reshaping their squad ahead of next season, with Jose Mourinho working alongside the club's hierarchy on streamlining the squad while adding elite-level talent.
Bernardo Silva has already completed a move to the Santiago Bernabeu and there is a strong possibility that Real Madrid will test Chelsea's resolve with an offer for Enzo Fernandez.
Should the Spanish side proceed with a bid for the Argentine, sources believe further internal changes would be required to accommodate another major midfield arrival.
That scenario could leave Tchouameni vulnerable despite remaining a highly regarded member of the squad. Sources suggest he may become one of the casualties if Real Madrid continue to strengthen in central midfield.
As things stand, he finds himself in a state of limbo, unable to be certain where he fits into the club's long-term plans. He fought with teammate Federico Valverde last season - and while that did not have direct consequences in terms of his future, his role at the club had already been in some doubt.
Manchester United's interest remains genuine, as they monitor what happens next. Club recruiters view the France international as a Champions League-calibre midfielder capable of significantly improving the quality of the squad.
Although there are reservations about signing players who do not have experience in Premier League football, United believe Tchouameni possesses the pedigree and profile to make an immediate impact.
The financial implications of any potential deal are expected to become clearer in the near future as United seek to establish whether a move would be realistic.
United continue to assess alternative midfield options and sources have told Flashscore that West Ham midfielder Mateus Fernandes remains a prime candidate to come in.
The problem is that other clubs are showing interest, and that is impacting their hopes of knocking down the £80 million being demanded.
Bournemouth’s Alex Scott is another name increasingly viewed as a realistic target should other pursuits prove difficult.
For now, however, Tchouameni remains a name to watch as Real Madrid's summer business develops.