Woodgate corrected a habitual problem in his joint with the operation at the end of last season, but is taking longer to recover than first thought.
"He is not into full training yet and with him we have to be a bit patient," Southgate said.
"The recovery from the operation he had could be 12 weeks, it could be 14 weeks.
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"That couple of weeks takes us into the start of the season, but we knew that was a possibility and fortunately it's a position we've got a fair amount of cover in."
Boro face Blackburn Rovers, Wigan Athletic and Fulham in the opening week of the 2007-2008 campaign.
Chris Riggott, Robert Huth and David Wheater are the men in the frame to start in the middle of the back four as Matthew Bates was seriously injured last week in a friendly against Darlington.
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