Gatland's stock is high after he guided Wales to the semi-finals of the World Cup in New Zealand last year, and he has previous Lions experience having been part of Sir Ian McGeechan's set-up in South Africa in 2009.
The Kiwi has named his 35-man training squad for Wales' upcoming Six Nations campaign, which included Gavin Henson despite the Cardiff Blues' back having just three games under his belt this season, but also cast his eye forward to 2013.
The Lions want their choice as head coach to be available to them on a full-time basis from a year prior to the tour, meaning Gatland would need to negotiate a release from his Wales contract, which runs until after the 2015 World Cup and includes a five-month break clause in the summer of 2013, in order to take the role.
But it is understood the WRU are open to negotiation over any approach, which would potentially allow them to develop a coach with a view to replacing Gatland when his contract expires.
When asked about the possibility of leading the game's most iconic touring side, Gatland said: "All I can comment on is last time I was involved it was a huge honour and if the opportunity came again it would be fantastic.
"I recognise the great entity of the Lions in terms of their history and if given the opportunity it would be fantastic.
"I think that Wales have always been incredibly supportive of the Lions and if there was that chance that the Lions wanted me to be involved then I don't think there would be a negative hindrance by the Welsh Rugby Union for me to do that.
"If I was offered any involvement I am sure they would be more than supportive."
For the time being Gatland's focus will be on maintaining the high standards set during that tremendous run to the last four in New Zealand, with Wales set to kick off their Six Nations campaign against Ireland in Dublin on February 5.
As has become the norm in recent years the selection of Henson provided one of the main talking points of Gatland's panel.
The 29-year-old, who has won 33 caps, has not played in a Six Nations since 2009, and has not featured for Wales since dislocating a bone in his wrist during the pre-World Cup friendly victory over England.
The former Ospreys, Saracens and Toulon man has played just three games for the Blues since joining them in October, featuring twice at full-back before playing in his favoured inside centre position against London Irish last weekend.
And Gatland warned he will have to prove his fitness at Wales' seven-day training camp in Poland next week.
He said: "There was a long debate about whether Gavin made the squad or not and it was more or less about us wanting to have a look at him on past performances and reputation and seeing where he is at.
"Like a number of players this is an opportunity for Gav to impress. Last time we were together before the World Cup he did well, he mixed it between filming 'The Bachelor' and playing a bit of rugby, but his attitude was great, he trained hard.
"I can only talk about Gavin in terms how he is in our environment and he has always been great and there have been no issues, so it's a matter will sit down with him next week and see where his head is at."
Gatland named six uncapped players in his squad, including 18-year-old Cardiff wing Harry Robinson.
Robinson caught the eye of Gatland while on Wales Sevens' duty, as well as during his handful of appearances for his region.
In-form Ospreys centre Ashley Beck, scrum-half Rhys Webb and the Scarlets trio of lock Lou Reed, prop Rhodri Jones and full-back Liam Williams are the other players yet to feature for their country.
Gatland has also included six players plying their trade outside Wales. France-based trio James Hook, Mike Phillips and Lee Byrne were all selected, as were Exeter prop Craig Mitchell, Saracens prop Rhys Gill and Sale back-rower Andy Powell, who will take part in three days of the camp in Poland as part of the conditions of their release from their clubs.
But there was no place for Scarlets fly-half Stephen Jones. The 34-year-old has won a record 104 caps for his country, but his latest non-selection following his omission from the squad to face Australia in December suggests his Test career may be at an end.
The first-choice lock pairing of Luke Charteris and Alun Wyn Jones, Scarlets' Rob McCusker, Tavis Knoyle and Josh Turnbull, and Newport Gwent Dragons hooker Lloyd Burns are all injured.
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