Defender Winston Reid has signed a new long-term contract with West Ham which commits him until the summer of 2021.
Blackburn have signed defender Doneil Henry on a month's loan from West Ham.
The Bosnian goalkeeper was strongly linked with a move up the Premier League food chain in January, with the likes of Arsenal and Manchester United said to be monitoring his situation.
Begovic ended up seeing out the January transfer window at the Britannia Stadium, but Stoke did move to secure the services of England international Jack Butland on deadline day.
That would suggest that they are planning for life after Beogvic, with a summer move widely touted.
The highly-rated 25-year-old is paying little attention to the gossip, though, with it important for him to end the 2012/13 campaign as positively as possible.
Begovic told SportSport: "I must confess it is nice to hear these things. It is always nice to hear what others are saying, it means that you are doing a good job.
"But I have no time to think about this. My only concern is Stoke City as I want to be as good as I can be for my club, and for my national team.
"So quite simply, I really don't have any time to think about a move or anything else."