Gatland has been linked with the job for the 2009 tour of South Africa, and the Welsh Rugby Union confirmed they would consider any approach from the Lions.
Wales currently do not have a senior tour arranged for that summer - but equally the WRU had their fingers burned when they allowed Henry to take charge of the 2001 Lions tour of Australia.
It proved the beginning of the end for Henry. Some of the Welsh players became disenchanted after they were overlooked for the Lions Test team and relations never recovered.
But Gatland has greater experience of northern hemisphere rugby from his stints as Ireland head coach and Wasps director of rugby.
He said: "Probably an advantage there would be over Graham Henry is that I have been in the northern hemisphere for so long - perhaps I understand England and Ireland.
"The Lions need to consider whether they go for someone local. It's flattering to be talked about. I suppose if we win a few more games everything is possible.
"But my first job is Wales and making sure this role is done and there's development to get Welsh rugby going. I have to think long term to the 2011 World Cup. That's my number one priority. I wouldn't consider the Lions until everything here is in place."
Gatland has entered the frame on the back of victories over England and Scotland but also because there are few obvious home-grown options.
England head coach Brian Ashton has already declared he will not be available for the Lions trip to South Africa, while Eddie O'Sullivan's stock has fallen since Ireland's poor World Cup campaign.
Wasps director of rugby Ian McGeechan is one of the favourites to be involved, 12 years after leading the Lions to their famous series win over the Springboks in 1997.
Both McGeechan and Gatland would bring the added bonus of a close working relationship with Shaun Edwards, the Wasps head coach who took up a part-time role with Wales to further his ambitions of being involved in the 2009 tour.
"It's one of the reasons he's taken the position here, because he'd dearly love to be involved with the Lions," said Gatland. "It will obviously help that we play South Africa on a couple of occasions before the Lions tour.
"At this stage it's more important to get Shaun involved with the Lions than myself. I would love for him to have that opportunity before myself."
The Lions are expected to select the head coach in May.