The Ligue 1 club, who finished third in the coronavirus-curtailed campaign and as a result qualified for the Champions League, rejected a initial bid of £18million for the 28-year-old but they may be tempted to accept an offer of about £25million.
Technical director Petr Cech, who played for Rennes before moving to Stamford Bridge, is an admirer of the Senegal international.
He will be expected to challenge for a starting position immediately with Kepa Arrizabalaga remaining out of favour following a catalogue of errors last season.
Mendy would be Chelsea’s eighth signing of the summer and take their spending to £225million.
Kai Havertz’s £72million move from Bayer Leverkusen was confirmed last Friday, following Timo Werner and Hakim Ziyech in a revamped attack.
Ben Chilwell has signed from Leicester City for about £45million, Thiago Silva has joined from Paris Saint-Germain as a free agent and Malang Sarr has also signed up as a free agent.
Xavier Mbuyamba has also joined on a five-year deal from Barcelona but is not ready for first-team football. Sarr is expected to head out on loan and Leverkusen have previously shown an interest in the young French centre back.
A number of departures are expected to be confirmed this week. Ethan Ampadu is joining Sheffield United on loan, while Tiemoue Bakayoko is heading to Milan with an option to buy included.
Danny Drinkwater, Davide Zappacosta, Kenedy, Conor Gallagher and Michy Batshuayi are also expected to have temporary moves confirmed.