The Daily Mail, as quoted by the Daily Mirror, is claiming that the west London side are considering making a move to land the French striker this summer.
Martial’s future at Manchester United has been something of a source of speculation due to his lack of playing time under Jose Mourinho this season.
The 22-year-old forward was limited to just 18 starts in the Premier League for Mourinho’s men, but still managed a decent goal return of nine strikes and five assists in the top flight.
Martial was left out of France’s World Cup squad for this summer’s tournament in Russia due to his stuttering form for Manchester United.
And according to the same report, Martial will be a target for Chelsea FC, even if manager Antonio Conte is expected to leave the club this summer.
Chelsea FC are likely to be on the lookout for a number of signings this summer as they look to build a team capable of winning the title next season.
The Blues ended the season on a high by beating Manchester United in the FA Cup final on Saturday.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news