Pulis insists the signing of Jack Butland in January does not mean Begovic will leave.
"Over the past two years Asmir has got better and better," said Pulis.
"No-one's rung me up to ask about him. They'd have to spend a hell of a lot of money to take him away. Chelsea tried to sign him a couple of years ago, at the end of his first season after joining us. I told him, 'You're not going'. He would not have got into the first team there and would have got lost in the system. As soon as that went away, he's been fine."