Gatland, 56, was in charge as the Lions and the All Blacks drew their three-Test series in New Zealand in 2017.
The former Wales coach says a fourth fixture could help rugby to generate revenue after the coronavirus crisis.
"It's potentially an opportunity to make four or five million pounds," Gatland told Sky Sport.
Ahead of next summer's tour, he raised the prospect of a meeting with the All Blacks as preparation, saying he had already spoken with NZ Rugby chief executive Mark Robinson about a game with the New Zealand Maori.
"But is it something the All Blacks... can do a bit of a decider [against the Lions] before we go off to South Africa end of June next year?" Gatland said.
Gatland, who stepped down as Wales coach in November 2019, will take 12 months out from his new role with Super Rugby side Chiefs for a third stint as Lions head coach next summer.
The Lions take on the world champions in South Africa for their first games against the Springboks since a series defeat in 2009.
However, rugby's plans are currently on hold amid the coronavirus pandemic with the recent Six Nations aborted, domestic and European club fixtures suspended and doubts over summer tour matches for Test sides.
The finances of respective unions are expected to be hit by the uncertainty, with Gatland also mooting the prospect of a tournament involving tier-one sides from both hemispheres as a way of boosting cash flows.
Gatland believes the enforced break could be an opportune time to assess the game's global calendar following much recent debate, adding: "I know the northern hemisphere is protective of the Six Nations because of how much money that generates and you can sort of understand that.
"I think there's potentially some opportunities for the world to come together in terms of how we get up and running again and generate as much potential revenue as we possibly can so that we don't damage what we've got.
"Looking at it, there's lots of different things going forward. In the November period, if the games in July and August are going to be called off, do the southern hemisphere teams go up to the northern hemisphere and play in a round-robin tournament where there's revenue sharing?
"I think potentially there's an opportunity to earn about £20million for each Home Nation if they did something like that."
Gatland spent 12 years with Wales before returning to his native New Zealand for the new Super Rugby season, but will take a sabbatical to return to Test rugby with the Lions, having also been in charge of the side for a series win in Australia in 2013.