The Blues are able to sign after having their two-window transfer ban lifted and one of the areas they want to recruit is up front.
Reports emerged that Dembele, who moved to Lyon in £20m in 2018, is a player Chelsea are very interested in.
And Sky Sports News claim that the Premier League side would be willing to pay €40m, which equates to around £34m.
The report also states that Chelsea had a bid of €40m rejected on Thursday.
Dembele has scored 30 goals since moving to Ligue 1 and Lyon are determined to keep hold of their player.
Lyon released a statement outlining their intentions to not let Dembele go.
It read: “Olympique Lyonnais has taken note of certain information relayed by the media suggesting that Moussa Dembele could interest other clubs during this transfer window.
“We would like to reaffirm its wish, as in the summer of 2019, to keep Moussa Dembele.
“The club has full confidence in Moussa and counts in particular on him to build a successful team for the seasons to come.”