It has been reported in recent days that United boss Jose Mourinho is making a renewed attempt to lure Willian away from Stamford Bridge, having also tried and failed last year.
Chelsea are well aware the 29-year-old fancies being reunited with his former boss at the Theatre of Dreams, with a fee of around £50m being mooted.
United insiders, however, have heard feedback any deal would not be straightforward as Chelsea are admirers of Martial and sense they can leverage the better end of any deal.
The France winger has hinted through his agent that he wants to quit United this summer after being forced down the pecking order following the arrival of Alexis Sanchez in January.
He also knows Willian is the player earmarked by Mourinho for the opposite flank and Chelsea intermediaries have suggested a stance in which they would accept a direct swap, something the Red Devils will not countenance given they value Martial closer to the £70m mark.