The 25-year-old has been in terrific form this year, but the imminent arrival of January signing Jack Butland has resulted in him being linked with a whole host of clubs, including Manchester United, Arsenal and Tottenham Hotspur.
However, Pulis insists that any potential suitors for the Bosnian would have to part with a large transfer fee.
"No, no-one's rung me up to ask about Asmir and if they did the price would be, I can't even think," Pulis told the Daily Star.
"They'd have to spend a hell of a lot of money to take him away. I couldn't even give you a price because I haven't even thought about it.
"The fact we've signed Jack doesn't mean we're going to sell Asmir. I still think there's more to come from Asmir. He's going to get better. He's been brilliant this year but there's still more to come."
Begovic joined Stoke from Portsmouth in 2010.