The Serbia international was linked with a move to Arsenal and Manchester United during the transfer window after the Potters bought England youngster Jack Butland from Birmingham City in January.
Stoke have made a promising start to the Premier League campaign under new manager Mark Hughes, and the 26-year-old shot stopper expressed his happiness at Britannia Stadium despite reported interest from Manchester City.
“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.”
Begovic also believes continued speculation surrounding the Serbian’s future will only serve to motivate the Potters goalkeeper.
“The interest motivates me even more and I would really like to become an even better goalkeeper,” he added.
“I’m a very ambitious guy but then again, I’m pleased with the club where I’m currently playing.”
Begovic has made 110 appearances in all competitions for Stoke after the shot stopper moved to the Potters from Portsmouth in 2010.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news