The Lions held New Zealand 15-15 at Eden Park on Saturday to end the series one-all, with the tourists drawing just their second series in history.
Head coach Gatland’s men rallied from their 30-15 first Test defeat to triumph 24-21 in Wellington in the second encounter, and edged to a gritty draw in Auckland to complete the trio of All Blacks clashes.
The Barbarians are slated to face the All Blacks at Twickenham on November 4 and Gatland admitted the Lions would fancy stepping in instead to take on New Zealand in an unofficial fourth Test.
Gatland said of the suggestion: “That would be good wouldn’t it? You’ll have to ask PRL (Premiership Rugby Limited) if they’d release any of the players.”
England had already explored the possibility of pulling rank on the Barbarians to face New Zealand in that November 4 encounter but the Rugby Football Union (RFU) eventually had to give up that ghost.
The notion of the Lions stepping in for a rare home fixture would appear a long-shot at this stage.
But it would not be beyond the realms of possibility for the Barbarians to look to reassemble the 2017 Lions squad, just in their black and white colours and not the red of the famed tourists.
The 1973 Barbarians were effectively the 1971 Lions reunited in different colours, and that star-studded side dispatched the All Backs 23-11 in Cardiff in one of the classic all-time matches.
For any kind of repeat, or indeed for the Lions to take the fixture instead of the Barbarians, the English club governing body Premiership Rugby would have to agree to release their players to take part.
Lions boss Gatland walked into the post-match press conference at Eden Park sporting a fancy dress red clown’s nose, in a pointed jibe at the New Zealand Herald.
New Zealand’s national newspaper had mocked up Gatland as a caricature clown in the wake of the Lions’ first Test defeat.
And New Zealand native Gatland was left unhappy with the media treatment in his homeland.
“The New Zealand public and fans have taken us to their hearts,” said Gatland. “It’s been a great series.
“What was disappointing for me was how much negativity was out there.
“I think we should embrace this concept of the Lions, I think it’s been brilliant. I think a lot of negativity turned the Kiwis off supporting the All Blacks.
“They were very much hoping that we’d do well and that as a team and a tour we’d embrace New Zealand.
“But that’s finished now, so we’ll just enjoy the next couple of days as a squad and reflect back on what this group of players have achieved.
“Some of these players have been on two tours now and are undefeated as Lions players. Those players who have been on two tours should be very, very proud of their achievements.”
Asked to explain the clown nose, Gatland added: “It was my idea.
“I had it last week but I didn’t think it was right time to wear it (after the second Test).”
The Lions’ only other drawn series came back in South Africa in 1955. New Zealand stretched their unbeaten run at Eden Park to 40 matches, but were left a little nonplussed by the draw.
Lions boss Gatland insisted he would not have wanted any extra-time to be played, and All Blacks head coach Steve Hansen agreed.
Asked if he would have wanted extra-time, Gatland said: “No. This is unusual, yeah, but I think those provisions have to be put in place beforehand.
“I spoke to Steve Hansen and he said it feels a bit like kissing your sister.
“For us to come here and draw a series in New Zealand it feels like some achievement, especially considering we were totally written off with the predictions for a three-nil whitewash.
“And this group of players have shown unbelievable character, it’s been a tough tour.”
When New Zealand boss Hansen was asked if he would have wanted extra-time, he said: “There’s no simple answer.
“Look, maybe everyone’s a bit hollow today because of the last three minutes.
“There was some really good rugby played, and maybe a drawn series was fair.
“We played well in the first Test, they played well in the second. We did well enough to win it in the third but they hung in there.
“So rugby’s always had a draw and it’s not a World Cup final; it is a three-match series. So my own belief is probably leave it the way it is.
“If you’re good enough to get a drawn series, both teams will get the credit that comes from it.”