Spurs boss Mauricio Pochettino signed a long-term contract extension this week and has been promised funds to strengthen his squad during the summer transfer window.
The Argentine manager is eager to add to his attacking options and Martial has emerged as a target.
United are willing to listen to offers for the Frenchman, who struggled for game time last season particularly after Alexis Sanchez's January arrival, but they are reluctant to sell to a Premier League rival.
However, the Old Trafford side are keen on Spurs defender Toby Alderweireld and that could work in Tottenham's favour in any negotiations for Martial.
Martial is likely to have offers from elsewhere as Juventus have also been heavily linked with the 22-year-old former Monaco man.