The Bosnian international, who is likely to make his season debut against Shrewsbury in Carling Cup action on Tuesday, was reportedly the subject of a Blues enquiry this summer as they seek back-up for Petr Cech.
But City manager Tony Pulis has since ruled out a transfer, and while pleased to have caught the attention of the Premier League champions, Begovic insists his primary focus is on life at the Britannia Stadium.
"Obviously I'm aware that the gaffer said there was an inquiry, but nothing is happening," Begovic told This Is Staffordshire.
"If someone wants to take me and they accept a bid, that's a different story, but in the meantime I just have to get on with my job.
"This kind of thing is just part and parcel of the job. Maybe there is people talking and stories being written, but at the end of the day you come to work
and do your job.
"On the other side, it is brilliant and I'm really flattered. Who wouldn't be if they were mentioned in connection with a great club like Chelsea?"
Begovic, who joined Stoke from Portsmouth in January for £2.25million, has lost out on game time to Thomas Sorensen so far this season.
But despite his frustration, the shot-stopper is determined to work hard to earn a regular spot in the team, and is looking forward to a run-out on Tuesday night.
"Of course I was very disappointed because everybody wants to play," he added. "All I can do is impress in training and in matches like this if I play.
"It would be nice to play in the cup because you don't want to let it be too long without a game."
Stoke suffered defeat in their opening two Premier League matches against Wolves and Spurs, but Begovic is confident the squad can overcome League Two opponents Shrewsbury, whichever line-up Pulis chooses to field.
"Even if you rotate the squad, we still have a good team, and that's a good sign of progress at the club," he said.
"It's a competition we take seriously, especially with Wembley and possible qualification for Europe at the end of it. But we must take it one step at a time."
Source: Team Talk
Source: Team Talk