The 40-year-old completed an unexpected move to Stamford Bridge from Premier League neighbours Fulham earlier in July.
And the Australia international concedes he had reservations about the amount of football he would play with Petr Cech firmly established as Chelsea's number one.
However, a conversation with new boss Mourinho rapidly allayed those fears.
"Before I spoke to the manager I had some doubts, but once I spoke to the manager those doubts disappeared pretty quickly," Schwarzer commented.
"The amount of games Chelsea play, there is going to be opportunities to play games and that's also important for me."
The former Middlesbrough stopper almost joined Arsenal in 2010, and sees no reason why he cannot push Cech for a starting place at Chelsea as he looks to keep himself in contention for a place in his country's FIFA World Cup squad.
"When I moved to Fulham, I thought that was it and then the Arsenal thing popped up so after that experience I said 'never say never,'" he added.
"It's proven to be true. I still say 'never say never'. It's not over until it's over.
"I am 40 years old but I feel incredibly fit and I love playing football. As long as I am playing well enough at this level I will continue to play.
"The aim is to continue to get better; I don't want to stop getting better. If you stop getting better then it is a downward slippery slope."
