Redknapp revealed on Tuesday that King is set to undergo surgery on a groin complaint, while Kaboul is expected to be sidelined for six weeks with a knee injury.
With Dawson missing and Gallas struggling with a hip knock, Woodgate could get the nod.
The former Real Madrid defender has only played two practice matches since his return and Redknapp admits he is taking a huge risk by considering fielding the former Real Madrid man.
"Woodgate is back in my squad which is a massive gamble for me, the club and for him,'' Redknapp said. "He could start. I have got him in my mind to throw him in at the deep end.
"I'll have a think about it today and see how he goes in training. He's not played a game of any significance yet but he is in my mind because he is such a fantastic player.
"I'm dreaming that he can come in and be somewhere near what he was straight away, which is not easy. We have some key, very important players missing so we have been pushed into pushing Woodgate in way in advance of what I should be.''
Redknapp says Spurs skipper King, who already undertakes a limited training programme in order to manage a long-standing knee problem, is really struggling
"Ledley will have an operation. He is nowhere near ready to play," he said. "He is supposed to be having the operation tomorrow (Wednesday). We'll see how it goes.''
King has not played for Tottenham since limping off during his side's 2-1 win at Fulham last October. Redknapp had hoped that the England centre-back would not require an operation on the groin injury which his manager thinks stems from his knee problems.
But King will now be missing for some time, meaning that Redknapp may end up pairing his only fully fit centre-half Sebastien Bassong with the returning Woodgate.
Redknapp added: "We have some key, very important players missing. ''Michael Dawson got sent off at the weekend, Younes Kaboul was in great form and then he was sent off for against Newcastle at home and now he has to have an operation on his knee so he's out.
"Gareth Bale and Tom Huddlestone are both missing. They are big players for us so we have been pushed into pushing Woodgate in way ahead of what I should be because we have problems with the squad.''