Woodgate is on the comeback trail from injury and with Spurs willing to let him head out of White Hart Lane on loan, he was given the chance to jump ship to Wolves.
However, the former Newcastle defender has opted against joining Mick McCarthy's relegation-threatened side at Molineux.
"He has been a world-class centre half and if he gets back to fitness he will be again," McCarthy said. "It seems he has made every effort to do that with the treatment he has had.
"If I thought there was a chance to get a player of his ilk, even for five, 10, 15 games, I thought it was worth doing but he wants to stay and fight for his place.
"He has not said it to me. There is some suggestion I have spoken to him, but I haven't. That is the message I have got."
Talented midfielder Kranjcar has found opportunities limited at Spurs this term due to the wealth of options available to Redknapp and Werder came forward with a bid.
Spurs made the Croatian aware of the offer, but the former Portsmouth midfielder has turned down the chance to talk to the Bundesliga side.