With Jorginho and N'Golo Kante both now the wrong side of 30, head coach Thomas Tuchel may give consideration to freshening up his options in the middle of the pitch ahead of 2022-23.
While Conor Gallagher is expected to be a part of the Blues first-team squad, there is a suggestion that Tuchel still wants to sign one more player for that position.
According to The Mirror, the Premier League giants have been monitoring the progression of Sangare, who has been impressing with PSV.
The 24-year-old, who is also an Ivory Coast international, has made a total of 47 appearances in all competitions this season, helping the Dutch club win the KNVB-Beker and push Ajax all the way for the Eredivisie title.
Although Sangare still has over three years remaining on his contract, it is suggested that Chelsea could get a deal over the line with a £30m proposal.
That is far cheaper than it would cost to push through the signing of Declan Rice with West Ham United insisting on a £150m asking price.