Warburton, who turned down the chance to captain Wales in their Six Nations victory over England last month, is the firm favourite to be tour captain after bookmakers suspended betting on him on Friday.
The 24-year-old said the decision to be Lions captain would be a “no-brainer” but confessed he had to ask his father Jez what it meant when the bookies said they were no longer taking bets.
“I didn’t understand at first, to be honest, because I don’t bet,” he said. “I didn’t know whether it was a good or a bad thing.
"My dad was the one who texted me. He loves it, my dad. I said, ‘what does that mean?’ He said there’s some inside information which has got out, or whatever.”
While Warburton is the leading contender for the post, Ireland second row Paul O’Connell and centre Brian O’Driscoll are also thought to be strong candidates for the post.
Warburton led Wales to the grand slam in the Six Nations last year when Lions coach Warren Gatland was in charge, but he is taking nothing for granted.
“One minute it’s O’Connell, the next it’s O’Driscoll, then it’s me,” Warburton said. “It’s difficult from a player’s point of view. I’ve heard about it and had everybody texting me, asking me what’s going on. I can only say, though, on my mother’s life, I’ve had no indication.
“The players are often the last ones to find out about these things. So, I’ll just keep my head down with the Cardiff Blues. As long as I can keep hopefully playing well, then the decision is completely out of my hands.”
Gatland has maintained that he has made up his mind over his captain but has not yet approached that person for fear of alerting the media.
Warburton, who lost the Wales captaincy during the Six Nations Championship, was offered it back ahead of the game against England when Ryan Jones withdrew through injury. But he turned it down to concentrate on his own game and prop Gethin Jenkins led Wales to the 30-3 win over England which clinched the title.
Despite turning down the leadership with Wales, Warburton says he would have no qualms about leading the Lions.
“It’s a no-brainer,” he said. “It’s the biggest honour any player could have. It’s mind blowing when you think about it – to have that accolade. Everybody who’s done it has been a legend and it’s very difficult and flattering to think that you’re even it contention for it.
“I still don’t see myself as one of those players, so it’s quite strange, especially at 24. If someone had told me when I was watching the last Lions tour that I could be a potential candidate, I would have laughed.
“When I talk about the Lions with my family I sometimes get a bit emotional. It’s because I’m so desperate to do it. I would absolutely love to have a jersey, framed up on my wall.
"That’s always been the goal for me, since I’ve been a young kid.”