He said the Lions hoped Jamie Roberts, Mike Phillips and Alex Corbisiero would be passed fit when the team is named by coach Warren Gatland on Wednesday ahead of its first training session in three days.
The Welsh pair of Roberts and Phillips have hamstring and knee injuries, respectively, while England prop Corbisiero has a calf ailment.
"We're hoping so, but the final decision will not be made until Wednesday," Irvine said on Tuesday. "The medics are reasonably hopeful, but we can't say for certain at this moment."
He said that Warburton had been carrying an ailment into the series, but had rebounded and was in strong form before tearing his left hamstring in the Melbourne match.
"In the first half of the second Test, I thought he was the most outstanding player on the park," Irvine said. "He is extremely disappointed at not being available.
"This is going to be one of the biggest games the Lions have played in the last 30, 40 years. We would dearly love to have our captain, and particularly when he's in such good form. So we can't hide from that, it's a big blow to us."
Irvine said the only positive was that the Lions were "fortunate in that it's one of the positions in the touring party where we have tremendous reserve strength." Either Sean O'Brien or Justin Tipuric will be selected at No 7, while veteran Brian O'Driscoll expected to take the captaincy.
The Lions haven't won a series since 1997 in South Africa, and O'Driscoll is desperate to break a personal drought of three previous series without a win.
Irvine, who played nine Lions Tests in the 1970s, defended the team's decision to base itself on the subtropical Sunshine Coast ahead of the crucial third test, saying the players needed time to recover after the physical and mental exhaustion of the first two tests.
The Lions are here for four days at a five-star resort and the players have had two days off training. The weather hasn't cooperated, however, with high winds, frequent rain squalls and generally unseasonably cool winter weather.
On Tuesday, the sun broke through the clouds for part of the day but the strong winds didn't let up.
"I've not got the slightest doubt - I've been on five Lions tours now and believe me after the second test the boys are physically and mentally exhausted," Irvine said. "They need a break. We have not had the best of luck with the weather ... but they need to recharge their batteries, and where better to do it than up here."
Irvine says the major news of the day on Tuesday - a second International Rugby Board hearing which cleared Australia captain James Horwill of stamping - was "water under the bridge ... let's move on."
Appeal officer Graeme Mew of Canada rejected the IRB appeal brought against Horwill after he was cleared of foul play charges at a previous judicial hearing by New Zealand-based Nigel Hampton, who found there was no intentional or deliberate action of stamping or trampling on Lions lock Alun-Wyn Jones in the first Test in Brisbane.
The decision was released on Tuesday, more than 14 hours after a two-hour hearing held late on Monday in Sydney by video conference and with Mew in Toronto.
"No great shakes as far as we're concerned. I'd just like to clarify that we had nothing at all to do with requesting the IRB look at it," Irvine said. "We were surprised as anyone when the IRB said they were going to investigate it.
As far as we're concerned, once a judicial officer gave his decision last week we were of the view that it was done and dusted. So it's really irrelevant as far as we're concerned."
The Lions won the first Test 23-21 on June 22 in Brisbane and, after being within one kick of clinching the series before losing 16-15 in Melbourne, are trying to end a 16-year losing streak.
The 34-year-old O'Driscoll, who made his debut as a Lion in the 2-1 series loss to Australia in 2001, figures no one is a certainty for inclusion in the side for the decider.
"Particularly when you have lost a game, I imagine every place is up for scrutiny, at least, as to whether the person deserves to be in the jersey again," O'Driscoll said.
"I won't go chewing my nails off thinking about it. I will go with the flow like everyone else does. Hopefully, I will be included in that team. If I am not, I will deal with that if the situation arises."
O'Driscoll said there appeared to be no favourite.
"We knew we were never going to get it easy against Australia, and it has been proved," O'Driscoll said. "They have been two incredibly keenly-contested games. Both of them should probably have gone the other way that they did, and it now culminates with a winner-takes-all.
"One more 80 minutes this season is all that is asked of everyone in the squad - the 80 minutes of their lives."