Bookmakers suspended betting on the captaincy after Warburton was backed heavily late last week, and the Wales flanker is expected to be unveiled when the squad is announced in London on Tuesday.
"I guess the favourite is Warburton, but for me it has to be Paul O'Connell," said Lynagh.
"He's done it before, he's a big guy, an inspirational bloke, fresh because he hasn't played much this season and is as fit as he's ever been.
"From a political point of view you have Scottish, Welsh and English represented in the management and no Irish. Appointing O'Connell would balance things up."
Lynagh subscribes to the view that for the first time a 'tour captain', who would not be guaranteed his place in the Test XV, should be chosen.
"I'd go down that route because it takes the pressure off who's going to be a certainty in the team," said Lynagh, who won 72 caps between 1984-1995.
"If he's not playing well, do you drop the captain? If you pick a tour captain then he has to perform during the opening three weeks of the tour to get in the Test team. That would be interesting."
O'Connell, who has missed most of the season with a back injury, became a genuine contender following an epic display for Munster against Harlequins in the Heineken Cup quarter-finals.
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