Gatland boasts an impressive record during his time in charge of the Lions so far, leading the team to a series victory in Australia four years ago before playing out a thrilling drawn series in New Zealand this summer.
The New Zealander could complete the trio of Lions opponents by leading the tour of South Africa in 2021, and while he insists his focus will be on Wales for the foreseeable future, he suggested that he could be interested in returning to the Lions for 2021.
"There's a lot of water to pass under the bridge before that. Eddie (England coach Eddie Jones) has put his name forward hasn't he? My focus is on Wales, for the autumn internationals and then looking towards the 2019 World Cup. I'm definitely finishing up there, unless they decide to get rid of me sooner!" he told reporters.
"So after that I might just go to the beach and put my feet up for a while. But you never say never. If there's a chat and opportunity to think about 2021, to do maybe the three as a head coach, to win two and draw one wouldn't be a bad achievement. I think once the global calendar is put in place then you need to look at where the Lions can fit in.
"This tour is unique and afterwards hopefully people can see the success of the tour, of the fans, the atmosphere, how brilliant it's been. I think if you were South African you would be pretty excited about the Lions coming in four years' time. There might need to be a little jiggling with the clubs in the UK and Ireland and to have one set of midweek matches. All we're asking for is them to do that once every four years."
Gatland, who is expected to be on the shortlist to replace Steve Hansen as New Zealand head coach after the 2019 World Cup, is only the second man to avoid a series defeat with the Lions against the All Blacks.