Reports last week suggested Arsene Wenger was considering a move for the injury-prone centre-half, but Redknapp insisted the England international is going nowhere.
"Is he going to Arsenal? No, not a chance. We wouldn't let him go to Arsenal," Redknapp said in the Telegraph, before joking: "I think they are after taking Sol Campbell back again."
Woodgate made his long-anticipated return to action in a training-ground friendly last week, and although the 31-year-old is out of contract in the summer, Redknapp has no intention of letting the former Real Madrid defender go.
"We want to keep him," he said. "He's out of contract in the summer, so if we let him out on loan then we're giving him away, unless he signs a contract before he goes. And you couldn't do that at the moment if he breaks down again.
"He needs to stay here. I love Jonathan, but it would have to be loaded as a pay-as-you-play deal. You can't have a boy who doesn't play all year and keep paying his wages."