Due to a bizarre contract, he needs to play three more Premier League games to trigger a clause for a one-year extension to his deal.
The former Newcastle man was always troubled with injuries during his time at St James' Park, and he has not played for Stoke since February.
Jonathan Woodgate: "I would like to stay, but it depends on the club.
"I am in no rush about it, so we'll see what happens. It was important I got games under my belt."