Full list of players available for Test by Wednesday
George North has an outside chance of being fit for the British and Irish Lions against the Wallabies in Saturday's opening Test, but Jamie Roberts is in "grave doubt".
The powerful Welsh wing has been struggling with a tight hamstring from last week's 64-0 win over the Combined Country, while compatriot centre Roberts has an injured right hamstring.
The tourists' head medical officer James Robson said North has been improving, but Roberts is battling to be fit to face the Wallabies in Brisbane on Saturday.
"George is an exceptional character and is working very hard with [physio] Phil Pask," Robson told reporters.
"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," he added.
Robson was less hopeful about Roberts's chances after he failed to complete Saturday's 47-17 victory over the New South Wales Waratahs in Sydney.
"Jamie is very well this [Monday] 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," he said.
"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 said he would deliver a full list of players available for Test selection to head coach Warren Gatland on Wednesday.
The team medic said he expected Irish centre Brian O'Driscoll to be fit along with England's blockbusting centre Manu Tuilagi.
Tuilagi picked up a shoulder injury during the 22-12 win over Queensland Reds and has not played since.
"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," Robson said.
But Robson said it was "highly unlikely" that Irish wing Tommy Bowe would be risked on Saturday after recent hand surgery.
"Tommy Bowe is running today [Monday] 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," Robson said.
"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."
The unbeaten Lions play against the Brumbies in Canberra on Tuesday.
The Test side will be announced on Thursday.