It is understood Begovic, 26, is rated highly at the Etihad and former boss Roberto Mancini was also keen on signing him.
But Begovic said: "I don't pay too much heed. All I worry about is working hard here.
"I am settled here and I am enjoying the work I am doing on a daily basis.
"I have a huge amount of faith in what the manager is looking to achieve here."
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