Hughes said the Bosnia-Herzegovina international would remain at the Britannia Stadium beyond the transfer window's close on September 1.
And the Welsh boss said he was keen to retain the services of Begovic, 27, but did keep the door open for an offer from a powerhouse club willing to pay for the custodian.
"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."
Hughes added: "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."
Hughes said he was also hoping to re-sign Begovic, who has two years remaining on his contract.
"I haven't seen too many keepers that I'd pick above him. I'd love to get him tied down," Hughes said.
In July, Stoke chairman Peter Coates said Begovic "can stay forever as far as I'm concerned" in a sign of the club's faith in their number one shot-stopper.
