The Daily Mail is reporting that Serie A champions Juventus are interested in a move to sign the France international in the current transfer window.
The same article states that Manchester United will only consider selling Martial if the 22-year-old looks to force through a move this summer.
According to the same story, the Red Devils will demand a huge transfer fee for the former AS Monaco forward after signing Martial in a £36m deal in 2015.
Tottenham Hotspur have also been linked with a move to sign Martial from their Premier League title rivals, although the Red Devils would be reluctant to sell to a direct rival.
Manchester United manager Jose Mourinho has used Martial sparingly since the Portuguese head coach took over the reins from Louis van Gaal two seasons ago.
Martial scored 19 times in all competitions under the Dutch head coach after the France international scored on his debut in a 3-1 win against Liverpool FC.
The Manchester United forward has struggled to hold down a regular starting spot since Mourinho took over the reins from Van Gaal in 2016.
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