Chelsea were reportedly interested in bringing former Arsenal goalkeeper Wojciech Szczesny to Stamford Bridge last summer.
According to the Daily Telegraph, Lampard was keen to sign Szczesny from Serie A giants Juventus, but the 30-year-old Polish international is settled in Italy and would not have been interested in a return to London.
Despite Chelsea signing Kepa Arrizabalaga for a world-record fee of around £72m in the summer of 2018, the Spaniard failed to assure Lampard that he was his long-term goalkeeper at Stamford Bridge.
Senegalese international Mendy has since offered more consistency and has become the team's new number one during the 2020-21 campaign.
Szczesny, who has won three Serie A titles and the Coppa Italia since joining Juve in 2017, has made 129 appearances for the club, keeping 53 clean sheets.