"I would love to go on tour and I've always respected the players who have gone on multiple Lions tours and that's something I'd love and try and do."
The New Zealand tour includes a total of 10 fixtures to be played from June 3 to July 8, including three tests against the All Blacks and five matches against New Zealand Super Rugby teams.
Warburton became the first Welsh captain for the Lions since 1977 when he led the side to Australia in 2013, a series won 2-1 by the visitors despite his absence from the final test through injury.
The squad for the New Zealand tour will be announced on April 19 and Warburton, who captained Wales for a record 49 games, is reportedly among the favourites to become skipper.
"Fans, pundits, media are all talking about it but I haven't had a single conversation about that," he added.
"You just know that's part and parcel of playing international rugby. It's a compliment but it's something I'm not thinking about."
(Reporting by Aditi Prakash in Bengaluru)
