Begovic has been a leading performer for Stoke in recent seasons, with his consistent form prompting frequent speculation over his future.
Liverpool and Real Madrid are among those to have been linked with the 27-year-old, who has 18 months remaining on his current contract at the Britannia Stadium.
Yet while Begovic is eager to progress in his career, he is not angling for a move away from Stoke, the club he joined from Portsmouth in February 2010.
He told Sky Sports: "I want to keep pushing forward. I've been here five years now, I feel I've progressed, improved as a player. I'm now getting to the stage of my career where I want to achieve things, win things.
"I've got some time left on my current deal; we'll see. We'll discuss things as time goes on.
"I've not had any discussions about my contract or an extension - that's usually done in the last 12 months of a deal. But I'm happy here, we are trying to build something here. We'll see what happens, but I hope to be a part of that."
Pressed on what would happen should a bid be made for his services, Begovic added: "I've got a great relationship with the manager and the chairman here. If things like that come up in the future I'm sure we'll discuss them.
"Football is a business at the end of the day. But I haven't really thought about it. I'm just focusing on my football, trying to improve as a player, and trying to get Stoke up the table."
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