Martial, currently in the United States on United’s pre-season tour, has a year remaining on his contract.
SSN understands Martial has told United boss Jose Mourinho he wants to leave the club after starting only 26 of his 45 appearances last season.
But it is understood United’s hierarchy are not interested in selling the France international forward, and could trigger the extra year option in his contract until 2020.
SSN understands Chelsea are yet to make a formal offer, while Sky in Germany are reporting that Bayern Munich would only make a move should United lower their valuation of the player.
Martial started United’s first game in the USA, against the San Jose Earthquakes, and could be forced into a significant role in the early part of the season.
Mourinho has hinted that Romelu Lukaku and Marcus Rashford could be used sparingly after their exertions in the World Cup this summer, leaving him with fewer options up front.
Should he make it to the Premier League opener against Leicester on August 10, only foreign clubs would be able to sign him, as the domestic window closes a day earlier.
Chelsea’s interest in Martial could prompt fresh questions over the future of Eden Hazard at Stamford Bridge.
Hazard has hinted he would like to move to Real Madrid after six years with the club, saying last week that “it might be time to discover something different”.
The move could also affect the future of another Chelsea forward – Willian.
Sky Sports News reported on Friday that Barcelona had lodged a third offer for the Brazil winger, but United were previously linked with a move for the 29-year-old back in May.