Wales insist they will never have another coach like Warren Gatland as they close in on appointing a successor to the New Zealander.

Martyn Phillips, the Welsh Rugby Union chief executive, believes the 10-year reign of Gatland, who will leave after the 2019 World Cup, is unlikely to be beaten in international rugby. The Scarlets coach, Wayne Pivac, and Glasgow’s Dave Rennie are the leading contenders to take on the role after Japan, but Wales’s shortlist extends to more than just two men.

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Only Phillips and the WRU chairman, Gareth Davies, know the identity of those in the frame but it is understood the former is an admirer of the Crusaders coach, Scott Robertson. An announcement is expected in the next few months.

“We will get the coach done this summer,” Phillips said, speaking on Wales’s summer tour of Argentina. “The shortlist is more than two and it’s the same one we’ve had for a while.

“We’ve been interviewing for a few years now and it’s been a combination of doing that, having meetings, and going for dinner. We’ve still got some more of that to do and then we’ll make the call. We’ve kept it very confidential between Gareth and I.”

Gatland was appointed coach in 2007 and has been in charge since, save for two sabbaticals when he was appointed as coach of British & Irish Lions. In that time he has won three Six Nations titles and two grand slams. Gatland is the most experienced coach in Test rugby history and is also unbeaten in two series as the main man with the Lions.

“I’d never say never, but I don’t think I’ll see another coach in my lifetime who will go 10 years with one team,” Phillips said. “Given where rugby is, I think it would be unusual to say the least for that to happen. I’m not sure anyone will match Warren’s legacy, that’s for sure.”

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The Wales players have also urged Gatland’s assistant Shaun Edwards to stay amid speculation linking him with a switch to England. The defence coach masterminded a tackling masterclass against the Pumas.

“The players are desperate for Shaun to stay. We enjoy working with him, he’s our defence coach and we’re giving everything we can for him,” the centre Scott Williams said. “As far as I know he’s staying.”