Anfield boss Kenny Dalglish is expected to sign a new centre-back before the end of August and has also been linked with Birmingham's Scott Dann and Bolton's Gary Cahill.
Reports regarding Shawcross joining Liverpool have increased since Pulis seemingly signed covering options in Jonathan Woodgate and Matthew Upson.
But ahead of Thursday's Europa League play-off at Swiss side FC Thun, the Stoke manager insists he has no intention of selling and only wants to add to his squad.
"We have got no need to sell Ryan," Pulis said in the Daily Mail. "We want to spend money if we can.
"I think the chairman and the board have made it quite clear that their intentions are to try to improve the squad this year.
"We are very pleased with the defenders we've got, now we have to improve our midfield and forward line."