The Blues are looking for a back-up to Thibaut Courtois with No.2 Asmir Begovic becoming increasingly frustrated at his lack of first-team opportunities.
So Chelsea will turn their attentions to Uruguayan Muslera.
Antonio Conte was keen on the 30-year-old in the winter transfer window but Galatasaray were not willing to sell.
But Chelsea have made the Turkish giants aware they will once again go in for their star man.
Muslera is out of contract at the end of next season which could make Chelsea’s task easier.
But Galatasaray are keen to extend his stay beyond the six years he has already been at the club.
If he was to leave this summer, the Super Lig side would want around £15m for his services.
Manchester United were interested in Muslera during Sir Alex Ferguson’s time at Old Trafford.