French publicaiton 'RMC Sport' claims that Spurs have seen a 'concrete bid' for the 21-year-old turned down by United, who are keen to keep the player.
Martial has been regularly linked with a move away from Old Trafford this summer after struggling to force his way into United boss Jose Mourinho's first choice line-up last season.
The player's name is believed to have cropped up during talks with Inter Milan over a move for Ivan Perisic but United would not entertain the idea of a move then and it is understood that nothing has changed on that front.
It is no secret that Spurs are on the lookout for a new forward player this summer, having previously been credited with an interest in Crystal Palace's Wilfried Zaha.
With a move for Zaha now all but off the table following the Ivorian's decision to sign a new long-term contract with Palace in May, Spurs have been forced to look elsewhere and it is believed that Martial is a serious target for Mauricio Pochettino's side.