Pulis has made no secret of his desire to strengthen his side's attack before the transfer window closes at the end of the month, but despite stories suggesting otherwise, the Potters chief says he is not in for the England international.
Crouch's future at White Hart Lane has been the subject of speculation for the last few weeks even though Spurs boss Harry Redknapp has done his best to dismissed those rumours.
The former Liverpool and Portsmouth star would also command a big fee if Redknapp did decide to let him move on and that would price him out of Stoke's reach.
Pulis told Sky Sports News HD: "No, we wouldn't be able to afford Peter Crouch."
Cardiff striker Jay Bothroyd was another name thrown at him during the interview but the Stoke manager refused to confirm his interest in him as the search goes on for a replacement for the injured Mamady Sidibe.
He was also given little away about the future of Tuncay who is rumoured to be on his way out of the Britannia Stadium.
He added: "I think [Cardiff boss] Dave Jones would be delighted you are touting his players around, but we will do our business the way we do our business and that is through the right channels.
"We were looking at four [signings] before Mama [Sidibe] got injured, but there will be players leaving as well and we are hoping the next 10 days will be a busy 10 days for everyone connected with the football club.
"Again there's been loads of speculation about loads of players leaving and for people to be moving on to do deals you have to have happy parties, have two clubs agree on deal and the player has to be happy to move.
"There is a lot of work that goes on behind the scenes and whether Tuny [Tuncay] is one of them we will have to wait and see."