Wales head coach Gatland insisted earlier in the week his current job was his priority but admitted it was "flattering" to be linked with the Lions role.
WRU group chief executive Roger Lewis has played down the link, saying: "When the story broke, I discussed it at length with Warren.
"We both agreed that the interests of Welsh rugby are paramount and if the Lions deflected from that in any way, the option would not be on the table.
"It's not really on the radar. Warren could have some Lions role, but we'd probably prefer it's not head coach."
Gatland's stock has risen dramatically since taking the Wales job in December.
The New Zealander has enjoyed the perfect start to his reign, masterminding RBS 6 Nations victories against England and Scotland in his first two games in charge.
Lewis said: "Warren's just starting with Wales and there are so many things we need to do.
"We're just looking at our next game against Italy at the moment, but beyond the 6 Nations there's this summer's tour to South Africa and the autumn internationals.
"The Lions are our partners, they're part of the heritage and history of Welsh rugby, and with Gerald Davies as their manager, we have great relations there.
"But if they came knocking for Warren, it would be our prerogative and right to block them."
The WRU could be discouraged by the unhappy experience of another New Zealander who led the Lions, Graham Henry, who took charge of the 2001 tour to Australia.
Henry was Wales coach at the time and took a large contingent of his players on the tour.
But when a number of them failed to make the Test team, it played a part in destroying his relationship with the Wales dressing room.
But another ex-Wales coach, 2005 Grand Slam winner Mike Ruddock, believes that should not necessarily rule out Gatland.
"I'm sure Warren could do a fantastic job with the Lions," said Ruddock, who was fulsome in his praise of the Kiwi's work with Wales.
"Henry's experiences with the 2001 Lions obviously did affect his relationship with the Wales players.
"But I think people will learn from that experience. It's a professional game, players should be able to put grudges aside and come back from a Lions tour ready to fight for their Wales place."
Wasps director of rugby Ian McGeechan is one of the favourites to be Lions coach, while South Africa's 2007 World Cup-winning coach Jake White has expressed an interest.
England head coach Brian Ashton has declared he will not be available for the Lions, while Eddie O'Sullivan's stock has fallen since Ireland's poor World Cup campaign.
Wales assistant and Wasps coach Shaun Edwards has been tipped to have some role in the Lions set-up.
Lions chief executive John Feehan said: "We have a process for naming the head coach where we review things after the 6 Nations and hope to appoint in April or May.
"We need someone with a sense of the tradition that goes with the Lions.
"We would prefer a British- or Irish-based person, but we're keeping an open mind - we want the best person for the role."