Martial is under contract at Old Trafford until 2020 but United are keen to tie him down to a new one following some standout performances for Jose Mourinho's side.
That has yet to happen, which has kicked off reports which suggest that both Chelsea and Italian giants Juventus, are keeping a close eye on the situation with a view to making a move.
Chelsea's desire to bring in more attacking reinforcements has been well documented and the young Frenchman showed his class with a devastating two-goal blast in the recent 2-2 draw between the two sides.
It was rumoured that Mourinho was willing to sell last summer only for the powers that be to rule out any such sale, and the decision has paid off as Martial is now starting to fulfil his undoubted potential.
United are unlikely to sell, especially to Chelsea, but the player's contract situation has the potential to make things interesting.