The highly-rated 26-year-old was linked with various top European sides over the close-season, but remained at the Britannia Stadium.
Although Stoke lie 16th in the Premier League following a run of three straight defeats, Begovic is satisfied he made the right decision in staying put.
"I'm happy because I stayed at Stoke City," Begovic told Mundo.
"I feel great here and I love my football here, but I can’t hide the fact that it was nice to be linked with so many big clubs.
"The interest motivates me even more and I would really like to become an even better goalkeeper.
"I'm a very ambitious guy but, then again, I'm pleased with the club where I'm currently playing."
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