The French giants were upset at being beaten to the punch for the striker when he joined the Red Devils from Monaco for an initial fee of £37.5m last year.
And United insiders have insisted the wealthy outfit won't need "much encouragement" if the starlet was to be put up for sale in the near future.
The 20-year-old's career has stalled this season under United boss Jose Mourinho, who has grown frustrated with his attitude and performances.
Martial hasn't made the most of his opportunities, this term, having scored 17 goals in his debut season with the club.
And the youngster wasn't even a part of the match-day squad for Sunday's 1-1 draw at home to West Ham United.
United are linked to a big-money summer move for Martial's France team-mate Antoine Griezmann.
The Atletico Madrid superstar is reportedly also a target for Paris, although they would not be too disappointed if it also did lead to Martial coming on to the open market.