Lions team manager Andy Irvine and chairman Gerald Davies expect to announce the head coach for the next tour shortly after this year's RBS 6 Nations, with all four Home Union coaches in the frame.
And Gatland, who led Wales to a World Cup semi-final three months ago, is keen to be given a second chance to taste series victory with the world's most famous touring team.
"I would love to be involved with the Lions again if the opportunity came up," Gatland told the Western Mail.
"South Africa was a wonderful rugby experience like no other. We went back to basics with an old-fashioned philosophy in a professional manner.
"It was a privilege to work with coaches and players from other nations and you learn so much."
Irvine has made it clear that the next Lions boss will need to be available for the entire year in the build up to 2013 and Gatland admits that may prove difficult given the fact that he signed a new four-year contract with the Welsh Rugby Union prior to the World Cup.
But even if national commitments meant Gatland was unable to take the role of head coach for the trip to Australia, he still hopes to be involved in some shape or form.
"One of the things the Lions would want from a head coach would be that person available for a certain period of time. That would mean the coach was not available for the 2013 Six Nations," added Gatland.
"It is not just about watching the internationals because you would have to keep in touch with the club games and it is a big job.
"Whether I could do that I am not sure and you would have to speak to (WRU chief executive) Roger Lewis. That would all depend on what was happening with Wales and that role is always going to be my main priority.
"If I was involved in the same role as I did in South Africa under Ian McGeechan, there would not be a problem because someone else is head coach and in charge.
"But there is still a lot of rugby to be played before any of these decisions are made."