He told BBC Radio Stoke: "We both want to play and we'll see what happens, but my intentions are obviously to play.
"Those are things that other people decide and I'm sure there will be talks over the summer. If I'm not playing, I'll be battling hard for sure."
Begovic joined the Potters from Portsmouth in February for £3.25m, but had to wait 25 April before making his debut for the club.
The Bosnia-Hercegovina international, 22, replaced the injured Sorensen in the first half against Chelsea, but could not prevent Stoke falling to a 7-0 defeat at Stamford Bridge.
It's going to take a lot of things to get the job done, but all the best to them
Asmir Begovic on Portsmouth's FA Cup final chances against Chelsea
He also conceded four goals against Manchester United on the final day of the season, although Begovic kept clean sheets in his other two appearances against Everton and Fulham.
Meanwhile, Begovic has said he will be watching his former club in action in the FA Cup final against Chelsea on Saturday.
"It's a big game for them and a tough task because Chelsea are on fire at the moment," continued Begovic.
"They've had a great run so far, they've knocked out some big teams, and on the day you never know what could happen.
"It's going to take a lot of things to get the job done, but all the best to them."
Begovic played in both ties for Portsmouth against Coventry in the third round, and in the victory over Sunderland in round four, before making the switch to the Britannia Stadium.
Source: BBC Sport
Source: BBC Sport