And after making history on the job, Irvine says the Kiwi has "every chance" of leading the tourists to take on the world champion All Blacks in four years time.
"These discussions will be taking place quite shortly, probably within the next few months," Irvine told Sky Sports' Rugby Club.
"I'm only one of a committee of four but I would certainly support it. I think Warren did a great job."
And Lions CEO John Feehan has added weight to these claims and has called Gatland an "outstanding candidate".
"Warren is the winning Lions coach and I am a big fan of him and I think he has done a fantastic job for us but, beyond that, it is still a decision that is two years' away," Feehan told the Telegraph.
"It is important to wait a year or two and then look at all the best coaches and draw up a shortlist of prime candidates.
"You then have to ask if they want to do the job, do they have the motivation and are they the right person.
"If you were picking it today, Warren would be the absolute outstanding candidate. He is a great guy, not just in terms of his rugby but how he managed to help us commercially. He is clued in a pretty much every level."