Full-back Stuart Hogg is thought to be in with a chance alongside winger Sean Maitland while loosehead prop Ryan Grant is in contention for a seat on the plane.
Glasgow head coach Gregor Townsend, who played in the last triumphant Lions tour, back in 1997, in South Africa, is upbeat about his players prospects.
He told the Evening Times: "We are very hopeful that there will be at least one Warrior on the plane for Oz and if that is the case then it would be a massive honour for the club.
"You would have to say that at full-back Leigh Halfpenny is the big favourite to start the three Tests, but as cover Hoggy must have a great chance of being in the frame after the way he performed in the Six Nations.
"I think the hard pitches over in Australia will also suit him and I would say the same of Sean Maitland.
"Both lads have real pace and I think if we really want to have a go at the Aussies they should be going because of the offensive threat they bring to the table.
"For me Ryan Grant also must have a great chance to go. He has been incredibly consistent for Scotland going right the way back to last summer's tour of Australasia.
"He maintained these levels in the Six Nations for Scotland and then a week past on Friday he more than held his own against Adam Jones.
"Not only is he technically a superb scrummager he is also outstanding in the loose.
"Again I think these are aspects that will hopefully be very much in his favour when the squad is announced tomorrow. So I will be saying my prayers."