The Premier League club have been in talks with Rennes over a transfer fee for Mendy, who is keen to join Frank Lampard’s side in this window.
The two clubs have been holding negotiations in an attempt to iron out various aspects of the deal for the 28-year-old goalkeeper.
Chelsea have now found a breakthrough in the deal and, according to French broadcaster Canal+, Rennes have accepted a proposal from the Blues.
The London-based club have agreed on a fee of €22m, plus €6m in bonuses, to sign the Senegal international from the Ligue 1 outfit.
Mendy has already to have agreed on a five-year contract with Chelsea.
The Blues are hopeful that the imminent arrival of the 28-year-old will also bring the best out of Kepa Arrizabalaga, who has struggled to establish himself as the number 1 following his world-record switch from Athletic Bilbao.
The two goalkeepers are expected to compete against each other for the spot in between the sticks at Chelsea.