The midfielder missed the 4-2 reverse at Chelsea last weekend with a groin injury sustained on Welsh international duty.
"It's not as bad as we first thought and he has an outside chance for Saturday," said Glenn at this afternoon's pre-Southampton press briefing.
Ledley King (hamstring) and Kazu Toda (calf) are also out but there is better news for Gus Poyet, Christian Ziege and Robbie Keane.
Glenn added: "Ledley's will be a little longer and he's having extensive treatment and Kazu is just about ready to join the squad in training after being out for seven weeks.
"It's looking healthier. Gus and Christian have come through their first reserve knock this week, Robbie Keane has had a good week's training.
"Christian has been out for about eight months now and definitely needs more reserve games and training. We won't throw him in that quickly because he's been out so long."
Glenn Hoddle says Simon Davies has an 'outside chance' of returning for Saturday's clash against Southampton.