After a series of high-profile errors, Kepa was dropped for the Blues’ final three games of last season.
The world’s most expensive keeper has struggled to live up to his £72million price tag since making the switch from Athletic Bilbao in 2018.
According to the Mirror, the club’s technical and performance director Cech is leading the charge to sign Mendy.
Efforts to recruit the 28-year-old are set to be stepped up this week and the report states that he will cost around £18million to prize away from the Ligue 1 club.
The Blues have already spent heavily as Frank Lampard orchestrates a dramatic rebuild of his squad.
Kai Havertz is the latest to walk through the doors, joining from Bayer Leverkusen in a deal worth around £70million.
The Germany international joins his compatriot Timo Werner, as well as Hakim Ziyech, Ben Chilwell and Thiago Silva as Chelsea’s major signings.
Ahead of their Premier League season opener away at Brighton on September 14, former Blues defender Frank Lebouef urged Lampard to axe Kepa.
‘It’s a real problem, he was very inconsistent last season and I think he [Kepa] has to go,’ the French World Cup winner told ESPN FC earlier this week.
‘When you’re a centre-half or a full-back, you need to have a comfortable presence behind you where you know that if you’re in danger the guy’s going to be behind you, saving you, which wasn’t the case last season.
‘So I think he has to go, but they have to find another one. It’s crucial for Chelsea to find a solution.’