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Chelsea had a verbal agreement for a five-year contract with Mendy,but have found it harder to come to an agreement over a fee for their primary goalkeeping target.
The Blues' previous bid was around €20 million (£18m/$24m) and it is understood that a fee will be reached somewhere between that figure and a maximum of €28m (£25m/$33m).
Mendy was seen leaving training with his agent on Friday morning and he went into an afternoon meeting with club president Nicolas Holveck to conclude discussions.
After today, the paperwork will still need to be completed with Mendy heading to London from the north of France for his medical.
"Edouard has an exceptional opportunity, humanly, we have to hear it," Stephan said to the French media. "But we must allow time for negotiations. A substitute? Obviously, we are looking."
Mendy spent just a season at Rennes, playing 34 games in their historic effort to earn qualification to the Champions League for the first time.
The Chelsea recruitment duo of Petr Cech, who now works as the technical and performance advisor, and Christophe Lollichon have heavily influenced the choice of Mendy, having come from Les Rouge et Noir to west London themselves.
With Kepa Arrizabalaga and Willy Caballero already in the squad, Mendy will arrive as competition for the pair over the No 1 spot with the Blues.
Kepa struggled last season in both shot-stopping and set-pieces, which has led to a loss of confidence that has impacted his displays and saw him dropped twice during the season.