Gatland spoke to the 33-year-old on Monday about making the trip to Australia but Wilkinson said he was committed to Toulon and that he was not sure if his body was up to touring.
However, Gatland said the pair will speak again in a couple of weeks, adding "if we do have an injury later in the tour we can have conversation then" about Wilkinson potentially being called up as injury cover.
On the subject of only choosing two fly-halves, Gatland said: "We just felt we wanted to give both an opportunity to get three or four games under their belt before the first Test.
"We've taken a risk and we admit that. Stuart Hogg can cover us there and if we do pick up injuries, we'll just have to call on a replacement."
Speaking about his captain Warburton, Gatland said he had "huge respect" for the 24-year-old, whom he appointed as Wales captain in 2011.
"For the last two or three years, he has been the most successful captain in the northern hemisphere," added Gatland.
Captaincy an unbelievable honour - Warburton
"It's a fantastically strong squad but if I think about naming the team tomorrow, Sam would be one of the players in there. He leads from the front."
Warburton said he had known he would be captain for "nine or 10 days".
"It's been the hardest secret I've ever had to keep, but I kept it in," added the 24-year-old. "It's unbelievable, it's an accolade which very few people can achieve. To be able to do this is an honour."
Wales supply four back rowers, with Justin Tipuric, Toby Faletau and Dan Lydiate joining Warburton and Ireland captain Jamie Heaslip on the plane.
England second row Geoff Parling tours ahead of fellow England lock Joe Launchbury, while there is no third fly-half option.
The likes of Scotland scrum-half Greig Laidlaw, Wales back James Hook and England inside centre Billy Twelvetrees, who could fill in at fly-half if needed, all miss out, with Scotland full-back Hogg viewed as the utility player who can step in at 10 when required.
Gatland added: "We've looked at the last few weeks in terms of performances. We've had a number of players who have come back from injury.
Lions down under 2013
Sat 1 June v
Wed 5 June v
Sat 8 June
Tue 11 June
Sat 15 June
Tue 18 June
Sat 22 June v
Tue 25 June v
Sat 29 June v
Sat 6 July v
"The benchmark for a lot of the squad was the Six Nations and then looking at some club form and assessing whether there was the same physical intensity to draw comparison and then finally make the selection of those players.
"If you look at previous tours, there are six to eight players who always get injured. There will be a key group of players who will potentially be called up."
Lydiate and Scotland second row Richie Gray both make the cut, despite injury-hit seasons.
Wales prop Gethin Jenkins is leaving Toulon at the end of the season and it is understood he will be released for the entire trip by the Heineken Cup finalists.
The Lions kick off their tour against the Barbarians in Hong Kong on 1 June, before flying to Australia for a series of warm-up matches against state sides ahead of the Test series against the Wallabies, which takes place on three consecutive Saturdays.
The Lions' last tour of Australia in 2001 ended in a 2-1 series defeat but overall they have won 75% of their games against the Wallabies, with 15 victories in 20 Tests.
Lions squad for 2013 tour
Leigh Halfpenny (Wales), Stuart Hogg (Scotland), Rob Kearney (Ireland), Tommy Bowe (Ireland), Alex Cuthbert (Wales), Sean Maitland (Scotland), George North (Wales), Jonathan Davies (Wales), Brian O'Driscoll (Ireland), Jamie Roberts (Wales), Manu Tuilagi (England), Owen Farrell (England), Jonathan Sexton (Ireland), Conor Murray (Ireland), Mike Phillips (Wales), Ben Youngs (England).
Dan Cole (England), Cian Healy (Ireland), Gethin Jenkins (Wales), Adam Jones (Wales), Matt Stevens (England), Mako Vunipola (England), Dylan Hartley (England), Richard Hibbard (Wales), Tom Youngs (England), Ian Evans (Wales), Richie Gray (Scotland), Alun-Wyn Jones (Wales), Paul O'Connell (Ireland), Geoff Parling (England), Tom Croft (England), Toby Faletau (Wales), Jamie Heaslip (Ireland), Dan Lydiate (Wales), Sean O'Brien (Ireland), Justin Tipuric (Wales), Sam Warburton (Wales).
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