The centre-half, who won the most recent of his 21 England caps against the United States in June 2010, has suffered an injury-interrupted career, but appeared in 20 of Tottenham's Premier League matches last season.
His latest lay-off intensifies Redknapp's problems in the centre of defence.
Dawson is serving a one-match ban after being sent off in Tottenham's 4-0 defeat by Fulham in the FA Cup fourth round and Kaboul is out for six weeks because he requires surgery on his injured knee.
William Gallas, who came on as a substitute in the wake of Dawson's dismissal on Sunday, is playing despite being hampered by a hip injury.
Cameroon international Sebastien Bassong is fit, while Bongani Khumalo, who is yet to play for the club since signing from South African side Supersport, and versatile full-back Vedran Corluka could be pressed into service alongside him.
Woodgate has not played since November 2009 after suffering groin trouble of his own.
But the former Real Madrid man has returned to light training and played in two practice matches against Charlton and QPR in Janaury.
"It is a massive gamble for me the club and for Woody for sure," said Redknapp.
"He has not played a game yet of any significance 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."
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