The Wales wing has been battling a hamstring injury he picked up in the 64-0 victory over Combined Country XV last week.
It had been reported that North would miss the opening encounter against the Wallabies in Brisbane but the Lions’ head medical officer, James Robson, has revealed he is in contention.
“George is an exceptional character and is working very hard with (physio) Phil Pask,” said Robson.
“He is back to running today and he is doing very, very well. An accurate assessment on his availability for selection will take place on Wednesday.
“At the moment he has a great chance of being fit for this week.
“We wouldn’t allow him to play if we felt he was at significant risk and we will only deliver (players) back to the coaches for selection when we are confident medically he is fine.”
The legendary Lions doctor was less optimistic however on the fitness of Wales centre Jamie Roberts.
The hulking centre also picked up a hamstring injury in Saturday’s clash with NSW Waratahs and has been rated in “grave doubt’.
“Jamie is very well this morning. His scan would indicate one thing, his demeanour would indicate another, but he is a grave doubt for this week, there is no doubt about that,” added Robson.
“You only had to see how much discomfort he was in at the weekend, however, further assessment will be made later in the week. He has tweaked or strained his hamstring.”
Robson will deliver a full list of players available for Test selection to head coach Warren Gatland on Wednesday.
Brian O’Driscoll and Manu Tuilagi are both expected to be passed fit, while Tommy Bowe could be back in contention for the second Test.
“Manu is progressing on a daily basis and was back into training the other day. He will be assessed medically as we go through the week before we determine his availability, but he is doing exceptionally well,” added Robson.
“Tommy Bowe is running today with a hand splint on. He is doing very well, and making remarkable progress, and we will get him reassessed by the hand surgeon later on this week.
“We will not allow Tommy to play unless we feel he is medically capable of playing. He had his small fracture stabilised almost a week ago and we are going to give him a couple of weeks to see how it goes.”
