The 32-year-old is a free agent after being released by Manchester United this summer, although his wage demands could make it difficult for Stoke to do a deal.
Pulis is also conscious that he already has five strikers on the books in Peter Crouch, Jon Walters, Mamady Sidibe, Kenwyne Jones and Cameron Jerome, and he would probably need to sell one of the latter two to make room for Owen.
The Stoke manager said: "Michael hasn't gone anywhere and it's still a possibility. There's still stuff happening and going on. Whether we can do a deal or not is another matter.
"I've always said he's a good player and someone I think people in the club would like to have around. He's a great professional as well and Crouchy has shown what great professionals can do for the football club."
Stoke have already signed three players this summer, winger Michael Kightly, midfielder Jamie Ness and defender Geoff Cameron.
Pulis is still hoping to add full-back Goran Popov on a season-long loan from Dynamo Kiev, but the Macedonia international has hit problems with his work permit.
Pulis said: "He's got to go to a tribunal on Wednesday so we'll see."
Whether Stoke can complete that deal or not, Pulis is confident there will be new faces at the Britannia Stadium before the transfer window closes in two weeks' time.
He said: "We're still looking to do some business if we can, and we always tend to do our business at the back end of the transfer window."