The former Portsmouth man has been linked with moves to both Old Trafford and Anfield although, as exclusively revealed by Goal.com, Liverpool are also eyeing Jack Butland, with Arsenal preparing to move for Pepe Reina.
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"It's very flattering," Begovic told Sky Sports News.
"It's positive feedback from other teams that people are looking at you and mentioning you with those teams.
"It's no secret that everyone has their own ambitions and they want to be playing at the highest level possible.
"But right now I'm just focused on taking Stoke forward and I think the club here has a lot of ambitions; the chairman, the manager and everyone else included.
"So we just want to keep pushing this club forwards and see how far we can take it."