Frank Lampard is still looking for a new shot-stopper after the poor performances of Kepa Arrizabalaga.
Rennes turned down an opening bid for Mendy, 28, but Chelsea have returned with an improved offer.
The English club have yet to receive a response from Rennes, who would prefer to hold on to Mendy.
The possibility of Mendy leaving was not a subject of discussion within Rennes at the start of the transfer window.
The Ligue 1 side have an ambitious project and are in the Champions League after finishing third last season.
Senegal international Mendy is an important part of Julien Stephan’s side, although missed Saturday’s win over Montpelleir for ‘personal reasons’.