Schwarzer, 41, joined the Premier League powerhouse on a one-year contract last year and largely played second fiddle to Petr Cech.
But Mourinho has been impressed with the Australian and another one-year deal is on the cards despite the reported return of Thibaut Courtois from a three-year loan to Atletico Madrid.
"I've had messages from the boss, he's very keen for me to re-sign with the club," Schwarzer said in Sydney.
"And that's all I really need to know - that he wants to keep me at the club and I'll leave the rest up to the powers-that-be to sort it all out. I'm confident it'll be sorted out in the next week or two."