The Sunday Times, as quoted by talkSPORT, is reporting that the Blues are looking into a deal to bring the 22-year-old striker to Stamford Bridge this summer.
Martial’s future at Old Trafford has been something of a source of speculation this summer after his agent hinted that the striker would be keen on a move away from Manchester United.
The forward struggled to hold down a regular starting spot in the first team at Manchester United under Jose Mourinho last season and that has prompted talk of a move away.
According to the same report, both Bayern Munich and Chelsea FC are keen on signing the former Monaco forward this summer as they look to bolster their attacking options ahead of next season.
The same article, though, says that Manchester United are expected to trigger a one-year extension to Martial’s current deal, which means his contract would expire in 2020.
Chelsea FC are thought to be on the lookout for a number of new signings this summer as they look to build a squad capable of winning the Premier League next season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news