The 41-year-old Australian said he has spoken with club management and revealed they are “keen” to bring him back to Stamford Bridge for another season.
Schwarzer spent last season as Petr Cech’s backup, appearing in just four Premier League matches.
Should Schwarzer’s words hold true, the move would further cloud an already murky situation for Chelsea’s keeper position next season.
Many believe Thibaut Courtois will finally take over for Cech as Chelsea’s top option in net, replacing the 32-year-old who has been a mainstay for the Blues for the better part of a decade.
But Courtois admitted on Tuesday that, despite having two years left on his Chelsea contract, his future with Chelsea is now unclear.
“My future seemed clear,” Courtois told Daily Express. “But then we played each other in the Champions League and that changed everything.”
Courtois, who has been on loan at Atletico Madrid for the last three seasons, said he would report to pre-season training at Chelsea and go from there. He also added that he isn’t thinking about a transfer right now and is focused on the World Cup, where he will serve as Belgium’s goalkeeper.
Should Chelsea decide to bring back Courtois, Cech would likely be the odd man out. He finished tied with Arsenal’s Wojciech Szczesny for the Barclays Golden Glove award with 16 clean sheets in 2013-14.