The 31-year-old defender is in talks with the Potters over a potential pay-as-you-play deal at the Britannia Stadium.
Woodgate is on the look out for a new club after being released by Spurs at the end of last season.
Premier chance: Jonathan Woodgate could be set for a move to Stoke after leaving Spurs
The injury-plagued defender has managed to play just four games in two years, which is why Pulis is keen on a appearance based deal.
Championship Leeds, where Woodgate began his career, were also believed to be interested in re-signing the defender, but he has expressed his desire to carry on playing in the top flight.
Stoke are also able to offer Woodgate better personal terms than Leeds.
Missing out on Woodgate, who made over 100 appearances for Leeds before joining Newcastle for ?9million eight years ago, would be a big blow to United boss Simon Grayson.
Grayson wanted the former Real Madrid and Middlesbrough star to form a central defensive partnership with the fit-again Patrick Kisnorbo and seal a rearguard that leaked 70 Championship goals last term.
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Source: Daily Mail
Source: Daily Mail