The hooker reckon Warburton is leading the race to wear the captain's armband in Australia but he insists the Cardiff Blues flanker must find his finest form.
"I think I would plump for [Warburton] as captain, he's a good player no doubt about that," Pullin told BBC Wales.
"He did lead Wales very well last year, what's happened to him since I don't know but you can't blame one person.
"If you're not playing well in that (the Six Nations), no matter who you are, then you shouldn't go on a Lions tour."
Pullin has backed his native England, who beat New Zealand in the autumn, to claim the Championship from Wales.
Wales have lost their last seven matches, since winning the Grand Slam and Pullin has been bewildered by the Dragons fall from grace.
"Obviously I'd have to say England, but I do believe they are a very strong side at the moment and I think they'll be the team to beat," said Pullin.
"Wales looked good last year but haven't been performing in the autumn internationals... I suppose the Australia game was a classic, how they lost that I don't know.
"When you've got a couple of seconds to go you should know what to do to hold onto a lead then, quite honestly.
"That really amazed me. All credit to Australia, they've scored in the last second and it was a good game, but good games don't count - you want to win them."