Over the past week, the two teams have each been frequently linked with players who represent the other side.
The Red Devils have been credited with an interest in Ben Chilwell and Raheem Sterling, the former no longer a target but the latter remaining on their radar.
Meanwhile, Chelsea are said to have made progress in their efforts to sign Jadon Sancho, despite Erik ten Hag claiming that the winger is more likely to stay at Old Trafford.
There is seemingly room for negotiations to advance on both sides, with Chelsea known to be eager to find a new club for Sterling among other things.
Nevertheless, according to Sky Sports News, United are seemingly more interested in discussing a potential deal for Chukwuemeka.
Chukwuemeka a surprise target
United officials are said to have explored whether it is possible to acquire the signature of the prospect before Friday's 11pm deadline.
Chukwuemeka seemingly started pre-season very much in the plans of Enzo Maresca, yet he has been provided with no game time since July 27.
Maresca has previously made the point of stating that he feels the 20-year-old requires a season where he plays in the region of 35 matches, rather than a bit-part role.
Chelsea are seemingly working to find a solution on Friday, even though Chukwuemeka may be brought back into Maresca's plans if he does stay.
The former Aston Villa youngster possesses a £40m release clause, that option being put in place when Chelsea signed him for £20m two years ago.
Would Chukwuemeka be any better off at United?
With Manuel Ugarte effectively replacing Scott McTominay once their respective deals go through, United are not necessarily any lighter in the middle of the pitch.
Chukwuemeka would, in theory, bring something different to Ten Hag's squad, yet the Dutchman already has Christian Eriksen and Mason Mount at his disposal.
With Eriksen available for transfer and Mount out injured, there may be an opening for Chukwuemeka to earn regular game time if he were to make the move to the North-West.