Gatland has won all five of his games since taking the Wales job

But New Zealander Gatland, 44, insisted his day job would have to come first.

"If there's a chance to get involved at some level that would be a huge honour but I have to make sure I don't neglect Wales," Gatland told BBC Radio 5 Live.

Gatland also backed the Lions claims of Wales assistant coach Shaun Edwards after their 2008 Six Nations success.

Interview: Wales coach Warren Gatland

The pair have a superb track record as a coaching partnership, with the Six Nations title coming in the wake of three league titles and a Heineken Cup during their time together at Wasps.

Their instant success at Test level with Wales has seen them talked up as serious contenders for major roles with the Lions.

"I'd love Shaun to be involved and he would relish that responsibility," said Gatland.

"He's a very proud Englishman who's working for Wales at the moment and we're delighted to have him."

See the full interview on Monday on BBC One at 2320 GMT

Edwards said he was excited by the possibility of transferring his successful coaching partnership with Gatland to the Lions stage.

"I think Warren would definitely go if asked and I'm sure he'd do a very good job," the 41-year-old told the BBC's Inside Sport programme.

"I'd like to put my hat in the ring - but not as a head coach."

Edwards has made no secret of his Lions ambitions, admitting his decision to join the Wales set-up - rather than take up a possible role with England's second-string Saxons side - was partly made with one eye on the 2009 tour.

"I did want to have a chance to go on the Lions tour," he added.

"I didn't go on the last one (to New Zealand in 2005) and, in my own mind, I had an excuse because I hadn't been involved in international rugby.

"If I don't go on the next one, I didn't want that to be an excuse."

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Inside Sport: Shaun Edwards

Speculation has also linked Wasps director of rugby Ian McGeechan with a role on the trip, and Edwards said he would be more than happy to work with his club colleague.

McGeechan led the Lions to their famous series win over the Springboks on their last visit to South Africa in 1997.

"It's not for me to tell the panel who to select, but I know the personalities involved and I know that the three guys (himself, Gatland and McGeechan) get on very, very well," said Edwards.

"It would be a unified coaching staff and that's very important."

Edwards and Gatland will get a chance to see the Springboks at first hand this summer with Wales travelling to South Africa for a two-Test tour in June before a return fixture at the Millennium Stadium in November.

Gatland said he would be anxious to avoid the mistakes of previous Lions coaches who allowed the job to impinge on their national team duties.

In 2001 another New Zealander, the then-Wales coach Graham Henry, led the Lions on their tour to Australia.

606: DEBATE I wouldn't be surprised to see Gatland and Edwards coaching the Lions Test side zl9t9n

Henry took a large contingent of Welsh players, but when a number of them failed to make the Test team it was widely seen as a factor in a deteriorating relationship with the Wales dressing-room.

"I'm not going to get ahead of myself - in the past other coaches have been involved with the Lions and haven't made their own job with their own nation the number one priority," he said.

"The Lions take up a lot of time and there's a lot of politics involved in picking the right team."

Last month Welsh Rugby Union group chief executive Roger Lewis suggested Gatland would be unlikely to lead the Lions to South Africa.

"It's not really on the radar. Warren could have some Lions role, but we'd probably prefer it's not head coach," said Lewis.