Begovic, who is contracted at the Britannia Stadium until 2016, has been linked with moves to both Manchester clubs, as well as Arsenal and Chelsea.
Speculation he is set to leave Stoke was fuelled in January when the Potters signed promising young England goalkeeper Jack Butland from Birmingham.
The Bosnia and Herzegovina international admits he does not know what will happen in the future but says his main priority is being at a club where he plays regularly.
"I'm a very ambitious person in life and in football and I want to keep trying to move forward," Begovic told The Sentinel.
"The club is desperately trying to do that, but it takes time and patience, so I don't feel I have become stale.
"If people are trying to move forward here, then I am happy to be a part of that.
"The main thing is to try to control your own destiny and do the best for yourself and your family."
He added: "The biggest thing is always to be playing. You are always passionate to play and if you don't have that game at the weekend it doesn't seem worth it.
"But what scenario will be thrown up in the future? You never know."
Begovic says he is trying not to focus on the ongoing speculation surrounding his future and instead concentrate on performing well for club and country.
"I guess I am used to all the talk now and obviously I am aware of the speculation," he said.
"I am just trying to keep my head down and fulfil my obligations to the club.
"I like to concentrate on my job and don't think too much about things outside of football.
"I am committed to the club cause and the national team."