Martial has just a year left on his current deal, but Chelsea and Bayern Munich have so far failed to meet Manchester United's asking price of £89.3 million, according to Duncan Castles at the Sunday Times.
The Red Devils do have the option to extend the 22-year-old's contract by another year. However, manager Jose Mourinho is "open to selling Martial and recruiting a specialist winger," according to the report.
Martial moved to Old Trafford from Monaco in 2015 but has failed to become a regular at the club. He made 30 Premier League appearances last season but 12 of those came as a substitute.
The Frenchman's agent, Philippe Lamboley, has said he wants to leave after failing to agree a new deal, per RMC Sport (h/t Mark Dobson at the Guardian).
Samuel Luckhurst at the Manchester Evening News said few clubs can afford Martial:
Chelsea may need to strengthen should they lose Eden Hazard to Real Madrid. The Spanish giants are keen on the Belgium international, but the Blues have no interest in selling, per Kieran Gill for the Mail on Sunday.
If United were to allow Martial to leave it would make more sense to sell abroad than to a Premier League rival. Mark Lovell at ESPN FC said Bayern have already been in touch:
There's a sense that Martial's career has stalled at Old Trafford. However, he may get the chance to stake a claim for a starting spot ahead of the new season.
Mourinho has said Manchester United will be without strikers Romelu Lukaku and Marcus Rashford for the start of the campaign due to their involvement at the 2018 FIFA World Cup, per Metro's Tony Mogan.
However, it may take something special for Martial to keep his place ahead of Lukaku. The Belgian scored 26 goals in his debut season for Manchester United and will expect to go straight back into the team.