The Daily Mirror is reporting that the west London club are looking to try and make a move to sign the Fulham striker after having been impressed by his recent performances.
Mitrovic has been in impressive form for Fulham since signing for them from Newcastle United for £22m in the summer transfer window.
He initially joined the Cottagers on loan back in January and struck 12 goals in 15 games to help them gain promotion to the Premier League.
The same story claims that new Chelsea FC boss Maurizio Sarri is unsure about the long-term future of Blues forward Olivier Giroud, who turns 32 later this month.
The article says that Chelsea FC will continue to keep tabs on Mitrovic as the January transfer window approaches, although his fine form is likely to have increased his asking price.
Meanwhile, Chelsea FC moved to the top of the Premier League table on Saturday thanks to a dominant 4-1 win over Cardiff City at Stamford Bridge.
The Blues are aiming to try and break back into the top four this season after having finished fifth and won the FA Cup last term under Antonio Conte.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news