The Bosnia-Herzegovina international has established himself as one of the best stoppers in the Premier League in recent seasons and Hughes believes that only a "top club" could lure him away, claiming any other move would see him go sideways.
"We don't anticipate any movement and it's not a decision to be had now," said Hughes, ahead of Stoke's Premier League trip to Hull City on Sunday.
"Our view is that he will be here and he will be our keeper. Our view is that if something was presented to us, we wouldn't be interested.
"It would be 'hands-off' if anybody came in. Hopefully we can keep him here for a long time.The thing with Asmir is that there's only a certain level he can go to now.
"It would need to be to one of the top clubs in the world. If he's going to move it won't be sideways.
"He is one of the best I've ever worked with and I've played with a few."
Begovic has two years remaining on his current contract and Hughes admits he is keen to open talks with the 27-year-old over an extension.
"I haven't seen too many keepers that I'd pick above him. I'd love to get him tied down," Hughes said.