The durable Australian goalkeeper hopes to agree another deal with the Blues but might have a new elite rival for a first-team berth next term
Schwarzer, 41, signed a surprise one-year deal with the Blues after leaving Fulham last year and impressed when called upon to cover the injured Petr Cech in the Champions League semi-finals and the final weeks of the Premier League title race.
Retired from international duty but still going strong in club football, the veteran spoke to Goal Australia on the red carpet at the Socceroos' official farewell dinner before the World Cup and said he hopes to be a part of Jose Mourinho's squad again in 2014-15.
"I would like to yeah," he replied when asked about extending his stay in west London.
"We've had positive discussions and I think it's just a matter of time now before something is concluded one way or the other."
With Schwarzer very much the reliable back-up keeper at Chelsea, it remains to be seen who will be wearing the number one jersey next season.
Much has been made of whether or not Mourinho will recall Courtois from his Atletico Madrid loan to challenge Cech, with Schwarzer hinting there could be a shake-up between the sticks next term.
"Maybe," he said when asked if Mourinho might choose to put his faith in the prodigious shot-stopper.
"Anything's possible at the moment.
"There's obviously a lot of things up in the air and a lot things will become a lot clearer (after) the Champions League final. And (then) we'll all know what's going to happen at the club next season."
Schwarzer came off worse in a clash with his younger counterpart earlier this month, as Chelsea bowed out of the Champions League at Atleti's expense. But he will be cheering on the 22-year-old Belgium international in this weekend's final against Real Madrid and at the World Cup.
"I said to him after the game when we played in the semi-final that I thought, first and foremost, that he was outstanding on the night but I also wished him all the very best firstly for the Champions League final and the league title (challenge), but also for the World Cup, it's an enormous few weeks for him."