The one-off "decider" would be aimed at raising funds for the game upon its resumption following the coronavirus pandemic that has let to economic crises for clubs and unions across the world.
The Lions - who drew their three-test series with the All Blacks 1-1 in 2017 - are due to begin their trip to South Africa in July next year, with matches against the world champion Springboks to come in Johannesburg (twice) and Cape Town in additional to tour clashes with the Stormers, Sharks, Bulls and South Africa A and Invitational sides.
Talks over a lucrative warm-up match on home soil in 2021 for the Lions had been reported well before the current shutdown, with Gatland revealing that the New Zealand Maoris had recently been suggested as a potential opponent by New Zealand Rugby chief executive Mark Robinson.
However, the Lions boss - who currently coaches back in his native New Zealand with the Chiefs after ending a 12-year stint in charge of Wales following the 2019 World Cup - appears to have his sights fixed on a high-profile clash with the All Blacks.
"But is it something that the All Blacks go up there for? A decider before we go off to South Africa at the end of June next year," Gatland told Sky Sports New Zealand.
"Potentially it's an opportunity to make 4 million or 5 million pounds from a game like that and put some money back into the coffers that we're going to need."