Redknapp said: "Aaron had another scan and it showed there could be a slight hernia problem.
"He feels he can get through it, so we're going to continue to train him for a couple of weeks, work with the physios and see how it goes. If after that he needs the hernia operation, we'll have it done.
"But he feels there's a chance he can get through. He could be back in a couple of weeks for us and that's what we're hoping for."
The normal recovery period from a hernia op is around six weeks.
If Lennon had surgery in mid-February, he would then be sidelined until the beginning of April - just a few weeks before England boss Fabio Capello announces his World Cup squad. The Spurs chief added: "It's a difficult one.
"He could have an operation on the hernia now but then he still hasn't recovered from the other problem with the groin.
"He's got the World Cup coming up. He might not need an op, if he can get away with it, then fine. We'll just see how it goes."