The Potters snapped up Butland in a £4million deal on deadline day last week and allowed him to stay with Birmingham City until the end of the season.
Begovic has since said he expects to be sold in the summer, with Manchester United touted as a possible destination, but Pulis says that will not necessarily be the case.
"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."
Indeed Pulis says that Butland could find himself loaned out for next season.
"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," he said.
"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."
Pulis also has Thomas Sorensen at the club - and the Dane is set to for talks on his future soon.
"I will speak to the manager to see what his vision is for the next few years," said Sorensen.
"The bottom line is that I am happy at Stoke, but what is pushing things the other way is my ambition to play. It is definitely something I will need to figure out because I obviously need to know where I fit in. If I don't fit in, then I will have to look after myself.
"No decisions have been made and I don't want to make a rash decision just because we are out of the FA Cup.
"I feel fit and ready. That's what you measure everything by - your motivation and your physical state.
"At the moment I feel good and I don't want to put any date on it (retirement) because I will play for as long as I can."