The 30-year-old King, who struggles to train because of knee problems, will have a groin operation and is "nowhere near being able to play" according to manager Redknapp.
A club spokesman confirmed on Tuesday that King would have surgery but said no date had yet been fixed.
With Michael Dawson suspended after his red card against Fulham, Younes Kaboul requiring knee surgery and William Gallas doubtful, Redknapp may have little option but to pick former Real Madrid player Woodgate in the Premier League at Blackburn Rovers in what would be his first start since November 2009.
"He's not played a game of any note but he's in my mind because he's such a fantastic player," Redknapp said of the 31-year-old who was not even named in the club's 25-man squad at the start of the season because of a groin injury.
"I'm dreaming he can come in and be somewhere near what he was straight away, but it's not going to be easy and I'll have to think about that one today.
"He'll be involved in some way but I've got a mind to throw him in at the deep end. I'll think about it [starting him] today and see how he looks this morning, but it's a big ask for him."
It is quite a turnaround for Woodgate who travelled to the United States and Australia in a bid to remedy the groin problem which limited him to three appearances last season and cast doubts on his career.
Tottenham, who are desperate to stay in touch with the top four, are also without Gareth Bale for the trip to Ewood Park because of a back injury.
