The France international is facing an uncertain future at Old Trafford following the appointment of Portuguese head coach Jose Mourinho back in 2016.
The 22-year-old struggled to hold down a regular spot in the Manchester United team since Mourinho took over the reins from Louis van Gaal.
Martial has been the subject of criticism for his inconsistent performances on the pitch to fuel speculation about his future.
Tottenham are rumoured to be interested in a potential swoop to sign the French striker in the summer transfer window to add some pace to their team.
Manchester United, on the other hand, are thought to be weighing up a swoop to sign Belgian defender Toby Alderweireld in the current transfer market.
Sky Sports News reporter Sheth believes Manchester United and Spurs could consider a swap deal involving Alderweireld and Martial.
“Tottenham interested in Martial,” Sheth the Transfer Talk podcast.
“They have a long-standing interest. Man United want Alderweirerld. I wonder could there be a swap deal.”
Manchester United finished in second place in the Premier League table last term to finish one spot above Spurs.
The Red Devils lost 1-0 to Chelsea FC in the FA Cup final at Wembley after Eden Hazard netted the winner from the penalty spot.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news