Mendy, 28, is admired by Chelsea’s chief goalkeeper Christophe Lollichon.
Lollichon himself had a spell in Rennes and made no secret of his admiration for the Senegalese national team.
Rennes have held talks with Chelsea as they seek to sign Fikayo Tomori on loan
And Chelsea bosses have now called for a deal for Mendy, according to the Daily Mail.
Lampard wants to continue adding to his squad this summer but is forced to scour the market for cheaper alternatives after already spending a lot.
Timo Werner and Hakim Ziyech have already been hired for a total of £ 80m and the expected arrivals of Ben Chilwell and Kai Havertz are likely to push their summer spending beyond £ 200m.
A goalkeeper and a central defender are Lampard’s next priorities.
Jan Oblak was the goalkeepers’ main target, but it will be too expensive, with Atletico Madrid demanding more than £ 100m for his services.
So Mendy emerged as a cheaper alternative.
Halfway through the pitch, Thiago Silva, the Paris Saint-Germain defender who will be involved in Sunday’s Champions League final against Bayern Munich, is a potential option.
Branislav Ivanovic was also considered for a surprise return, but Chelsea opted for a move against the Russian.
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