The Potters have been linked with the 32-year-old ever since he became a free agent after his release from Manchester United this summer.
Pulis wants to sign the former England international on a pay-as-you-play deal.
"I would love to sign Michael," he told The Sentinel. "If we can do it, we will do it, and do it on the basis that we did with Jonathan Woodgate and players like that.
"If he's in the team he will get paid, and if he isn't he won't get paid so much."
As the striker is out of contract he can be signed outside of the transfer window and now it has closed until January that has made him more attractive to other clubs, with Sunderland and Liverpool now being linked.
- Jonathan Woodgate
- Manchester United