Woodgate has not played first-team football for more than a year due to a groin injury that was so serious there were fears his career could be over.
He is now back in training and rebuilding his fitness, but remains a long way down the pecking order behind the likes of William Gallas, Michael Dawson, Sebastien Bassong and Younes Kaboul.
Harry Redknapp: "I'm happy for him to go if he wants. It's really up to him.
"Jonathan's played a couple of games for the reserves and in training games - but now we really need to see him move up a gear.
"He definitely needs to get some proper first-team games under his belt."