The France international, who was not apart of Les Bleus' World Cup-winning squad, has been linked with a move to Tottenham for much of the transfer window so far, with Spurs centre-back Toby Alderweireld touted to go in the opposite direction.
Alderweireld's future remains up in the air, but The Telegraph have claimed that the Lilywhites are hopeful of signing the 22-year-old irrespective of what happens with the Belgium international.
The report goes on to state that the Red Devils will strengthen their position on Martial - whose contract expires next summer - by triggering a one-year extension.
The former Monaco starlet, who joined United in 2015, is valued at around £45 million, according to The Telegraph. At that price, he would be Spurs' most expensive-ever signing.
Tottenham are also said to be interested in Wilfried Zaha but it remains to be seen whether there is enough room - and money, given Zaha is worth £60 million [The Sun] - for both attacking players in Mauricio Pochettino's squad.