Begovic has been linked with a big-money exit from the Britannia Stadium for some time, with clubs in England and across Europe closely monitoring his situation.
Stoke have been able to keep the transfer vultures at bay, but speculation is intensifying again ahead of the winter window.
City are the latest side reported to be readying an approach, with it suggested that England international Joe Hart - currently out of favour at the Etihad Stadium - may be offered to the Potters on loan to help cover their goalkeeping loss.
But despite being flattered by the link, Begovic insists he is happy to focus on his role at Stoke.
"You know there's compliments and obviously positive things and I use it as motivation, things like that, but I don't pay too much particular attention to different reports I just concentrate on my job here, each and every day," he said.
"If people are saying nice things it obviously means you're doing something right on the pitch, that's all I'm focused on.
"I want to maintain my performances and help the team win, that's my job and what I'm focused on, and like I said I'm happy to do so."
City boss Manuel Pellegrini was quick to play down such talk on Tuesday, and Stoke chairman Peter Coates claims he too is unaware of where the rumours have emanated from.
He told The Sentinel: "This latest story was certainly news to me and I suspect it is just a bit of speculation. That's my guess, anyway, and we have certainly had no approach.
"He is a top goalkeeper, so this kind of thing is going to happen. We are just concerned that he concentrates on playing for us and doing what he has been doing up to now.
"It is important we keep him for the rest of the season. It is an important season and he is a key player. He certainly hasn't made any noises."
Coates has also been reflecting on Stoke's much-needed victory over Sunderland, which lifted them three points clear of the drop zone, and looking ahead to a trip to Everton on Saturday.
He added: "We needed to break that cycle of not winning in the league and so it was an important win in that context.
"We have not been playing badly, but that sort of thing can become a psychological barrier.
"Everton away is certainly a tough game, as they all are, and they are having a good season.
"I always enjoy going there because of the kind of club it is, but also because we always seem to give a good account of ourselves there."