Woodgate signed for the Potters last summer on a free transfer from Tottenham, but City took no chances on the 32-year-old, handing him only a one-year deal, but with the guarantee of an extension should he make a certain number of appearances.
With 21 matches behind him for Stoke, Woodgate needs to play in just three more games to assure himself of a place in the squad for next season.
Tony Pulis: "If he doesn't get the games in that doesn't mean we aren't going to offer him a new contract.
"Woody has been brilliant, playing in a lot more games than people probably thought he could play, and he's good to have around.
"He's been very good for (Ryan) Shawcross and (Robert) Huth in lots of respects.
"So let's get the season out of the way and then we'll sit down and discuss everything with (chairman) Peter (Coates) and the family."