Martial's time at Old Trafford could soon come to an end, following the arrival of Cristiano Ronaldo this summer, and Spurs are understood to have expressed an interest in the 25-year-old.
Ndombele, meanwhile, was linked with a departure over the summer and Ole Gunnar Solskjaer's side have recently emerged as a club monitoring the midfielder's situation.
According to the Daily Express, United are open to selling Martial for around £40m, however Spurs believe they can persuade the Red Devils to agree to a swap deal for the forward involving Ndombele.
Ndombele, 24, has featured in each of Tottenham's last three matches across all competitions, but it is thought that the midfielder is unhappy at the club and is looking to move on.
As for Martial, he has started in just two of United's five matches in all competitions, with the likes of Ronaldo, Mason Greenwood and Edinson Cavani seemingly ahead of him in the pecking order.