Stoke City manager has told Sky Sports that the keeper will not leave this summer, despite interest from Manchester United.
Stoke City have also signed Birmingham and England goalkeeper Jack Butland in a £4m deal last month during the January transfer window, and he could replace Begovic as Stoke’s number one next season.
Pulis has claimed that this might not be true.
“If Manchester United come in and offer an enormous amount of money or someone else does, we would have to look at it,” said Pulis.
“But I haven’t brought in Butland because of that.”
The Potters’ boss has also revealed that Butland might join Birmingham on loan next season as well.
“If it comes to next season and we’ve still got three goalkeepers and feel Jack isn’t ready, he’ll be loaned out again,” Pulis continued.
“There was no thought in my mind of bringing Butland in just in case Asmir went. We felt it was a fantastic opportunity. The price was unbelievable.”
Begovic has become one of the top keepers in the Premier League and he could replace David de Gea at Old Trafford next season.