Owen is available on a free transfer after being released by United at the end of last season and Pulis has spent the last few months trying to persuade the former England, Liverpool, Newcastle United and Real Madrid star to join his team.
The 32-year-old's wage demands have made it difficult for Stoke to do a deal and Pulis knows he would probably have to sell one of his current strikers to free up cash for Owen, yet he believes the move could still happen.
"Michael hasn't gone anywhere and it's still a possibility," Pulis said on Friday. "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 (Peter Crouch) has shown what great professionals can do for the football club."
Stoke have already signed three players -- winger Michael Kightly, midfielder Jamie Ness and defender Geoff Cameron -- during the close-season.
Pulis is willing to wait until late in the transfer window, which shuts on August 31, before ruling out a deal for Owen.
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," he added.