Mendy's arrival will increase the pressure on Kepa Arrizabalaga following the Chelsea goalkeeper's howler in Sunday's 2-0 defeat to champions Liverpool in the Premier League.
"Yes, Mendy is having a medical as we speak. Subject to that being OK then he will become our player," Lampard said.
"With Mendy, it is more competition and it will push Kepa himself to be in this team."
Mendy, 28, will move to the Premier League after spending one season with Ligue 1 side Rennes, whom he helped finish third and qualify for the Champions League. He made 33 appearances in all competitions during the 2019-20 season, keeping 13 clean sheets and helping Rennes to the joint-second-best defensive record in Ligue 1.
ESPN reported earlier this month that Mendy will join in a deal likely to be worth an initial £18 million and rising to as much as £25m.
Chelsea have been in the market for a goalkeeper after Lampard was left unimpressed by the performances of Kepa, who joined the side for a world record €80m fee in 2018. Willy Caballero had become Lampard's preferred No. 1 towards the end of last season and sources told ESPN that signing a new keeper this summer was a priority for Lampard.
Lampard also confirmed that Caballero will start in goal against Barnsley in the Carabao Cup and that the decision was taken before the defeat to Liverpool last Sunday.