The Bosnia goalkeeper has been widely tipped to make a move to a Premier League heavyweight this summer, with speculation surrounding his future having intensified since the winter window.
Stoke's decision to snap up England international Jack Butland from Birmingham City in January was considered to be a sign that they are preparing for life after Begovic.
Pulis, though, is adamant that any potential suitor will have to dig deep in order to tempt the Potters into parting with their highly-rated shot-stopper.
He said: "No-one's rung me up to ask about Asmir and if they did the price would be... I can't even think.
"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.
"Asmir over the past two years, has just got better and better. I really do think he's a top goalkeeper."