New Zealander Gatland will leave his post after the World Cup in Japan later this year, ending a reign highlighted by a Six Nations record three Grand Slams.
He has already been linked with succeeding Eddie Jones as England boss, possibly moving to France and heading up the 2021 British & Irish Lions tour of South Africa.
Asked if he could see Gatland coaching England or France, Jones said: “I think we have got him on residency now haven’t we, so he can’t.
“In professional sport, you never say never.
“I am sure he will have a little bit of time off and take a break away from it, I should imagine, and then decide what he wants to do. If he does, we wish him well.”
Jones, Gatland and Wales’ Six Nations title and Grand Slam-winning players were greeted by about 1,000 fans on the Senedd steps in Cardiff Bay during a reception hosted by the National Assembly for Wales and Welsh Government on Monday.
It came just 48 hours after Wales claimed their first Grand Slam for seven years and first Six Nations title since 2013 by beating Ireland 25-7 in Cardiff.
Asked about Gatland and the 2021 Lions, Jones added: “If you are asking if his hand is up for the running, it is going to be, isn’t it?
“When you have the experiences he has had in the last campaigns, in particular with the Lions, his name is going to be bandied about in those realms.
“There are other coaches’ names that are going to be in the ring as well, but it is easy as a player – you can just sit back and watch that sort of stuff.
“There will be a few people with even bigger selection headaches than the coaches do.”
Wales’ Six Nations triumph means they will head to the World Cup as major title contenders, and they are already being tipped by many pundits to at least match their semi-final achievement of 2011.
Josh Adams, Alun Wyn Jones, Hadleigh Parkes and Liam Williams are four of our #GrandSlam heroes up for #GuinnessSixNations Player of the Championship! Full story: https://t.co/2RrIGu79wE— Welsh Rugby Union 🏉 (@WelshRugbyUnion) 18 March 2019
VOTE HERE 🗳️ https://t.co/gKIpOTWTP4 pic.twitter.com/0Mf8aAxyN0
“It is very easy for other teams now to say we are going to be putting our hands up, to take the pressure off themselves,” Jones said.
“People will pick apart the deficiencies we still have in our game. If we didn’t have that, there would be no point in us being here.
“We are well aware of that, and Gats is always a coach who puts us under pressure and challenges us, irrelevant of games.
“Everyone dreams – we all dream – but there is work still to do. We are comfortable with the deficiencies we have, and we will work on them. We will see what happens.
“We have had a bit of luck (in the Six Nations) – whether it was a bounce of the ball or a decision a referee has made.
“We are not going to bemoan the fact that we did have a bit of luck in the competition, but a lot of graft went into our performances, even though at times we were unconvincing and let opportunities slip.
“We have been very real about that for the entire campaign. I said in the post-match (after Ireland) there is a lot you can do with a bit of hard work and luck. In its simplest form, that is what we showed.”
Gatland, meanwhile, told supporters: “I promise you that these guys will give 100 per cent in every game at the World Cup, and if we play as well as we have for the last year, then we can bring home the World Cup.
“I know that these guys won’t go down in any match without a fight. You need a little bit of luck and hopefully we don’t pick up too many injuries.
“I assure you that we will go there with some confidence and belief that we can have a great tournament.”
And when a supporter in the crowd advised Gatland not to go to England, he replied: “I would never be allowed back across the Severn Bridge.
“I’ve loved it here and there are no plans at the moment. I am going to finish the World Cup and take a break. Then maybe, with a bit of luck, somebody offers me a job.”
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