According to Goal, Chelsea have made an improved bid of €20 million (£18m/$24m) for Rennes goalkeeper Edouard Mendy.
The Blues reportedly submitted a first offer of €17m (£15m/$20m) for Mendy last week but the bid was rejected by the French club.
Chelsea boss Frank Lampard is keen on signing a replacement for Kepa Arrizabalaga, following his struggles in goal for the Blues last season. Chelsea made Kepa the most expensive goalkeeper ever in 2018, paying £72 million ($93m) to bring him to Stamford Bridge from Athletic Bilbao.
Rennes are determined to hang on to the 28-year-old Mendy after the Senegalese international helped the French club secure Champions League football with a third-place finish last season.
The Blues have already brought in a host of new faces ahead of the start of the season including Ben Chilwell, Timo Werner, Hakim Ziyech, Malang Sarr and Thiago Silva.