Gatland was speaking after his side lost to South Africa 19-16, a day after England beat the All Blacks 19-7 in the Rugby World Cup's first semi-final.

The England coach responded by telling reporters: "You just send my best wishes to Warren to make sure he enjoys the third and fourth place play-off."

England face South Africa on Saturday.

Gatland and Australian Jones have had a long-standing rivalry. Prior to the quarter-finals, the Kiwi suggested Jones was wrong to use the "do-or-die" mantra in relation to England's match against Australia because it was said in the aftermath of Typhoon Hagibis, which left at least 82 people dead.

At the weekend, Gatland added: "We have seen in previous World Cups that teams sometimes play their final in semi-finals and don't always turn up for a final.

"So it will be interesting to see how England are next week and it could be a good game."

'Farrell will be fine'

Meanwhile, Jones said Leicester wing Jonny May was recovering well from the dead leg he suffered in the 45th minute during Saturday's victory.

"We had a walk through this [Monday] morning and we had to tell Jonny to slow down a bit," the England coach said.

But May is in "immeasurably better" condition than when he was recovering from a hamstring problem at the same stage last week, Jones said.

Fly-half Owen Farrell also picked up a dead leg in the first-half against New Zealand, leaving George Ford to take over the kicking duties.

Jones added: "Owen's a bit sore but he'll be fine. We've got a few others carrying bumps and bruises because it was a tough old game."