The Lions legend, player on two tours and coach on five, has been hugely impressed with the Cardiff Blues flanker's resurgence.
Warburton relinquished the Welsh captaincy, with former Lions Gethin Jenkins and Ryan Jones also wearing the armband during the triumpant RBS 6 Nations.
But McGeechan insists leadership qualities do not go away and believes Warburton proved his class against Scotland and England.
"For me Sam Warburton has come through strongly," McGeechan wrote in his Daily Telegraph column.
"The biggest question mark hanging over him was his ability to stay fit.
"It was not an indictment of Warburton for him to be held back from the Wales captaincy. Rob Howley did exactly the right thing.
"What gets you on the plane for the Lions is playing well. Leadership qualities never go away. Your form or fitness can. His last two games have answered all the questions.
"You would have to talk about Brian O'Driscoll in that captaincy conversation, Chris Robshaw as well.
"In the first part of the tour, Warren Gatland will give every player an opportunity so you need good leaders every time you put out a side.
"You try to implement the same principles of play so that it becomes second nature to the group. That requires strong, collective leadership. Sam Warburton is my front-runner."
The 2013 Six Nations may not have been a vintage tournament but McGeechan reckons there is plenty to be positive ahead of the trip Down Under, and singled out the performances of former Lions Mike Phillips and Jamie Roberts.
"I am encouraged by what I have seen. Some say it has been a middling Championship but that does not have to be a concern.
"I am not downhearted at all. The Lions is all about chemistry, about matching players with other players and seeing one work off the other. You cannot look at players or teams in isolation.
"Ireland have not had a great tournament but how would their No8 Jamie Heaslip fare if he were put between Sam Warburton and Justin Tipuric? Pretty well, I would say.
"We have seen enough to know that the Lions will trouble Australia. It was great that the Championship finished on a real high at the Millennium Stadium, with big-game players such as Mike Phillips and Jamie Roberts, both Lions in 2009, really stepping up. Wallabies take note."
"They came into their own. Big, intelligent men running hard. That is how you squeeze Australia. It starts in the front five, through to the back-row and midfield. If you get that right, then you are in business.
"As for attacking potential, the players are there. The hard grounds of Australia will draw the best from players like Roberts, Rob Kearney, George North, Jonathan Sexton and others."