Talay has expressed his interest in the national team job, which has become available after Danny Hay was released at the end of his contract.
Phoenix chief executive David Dome said the club was behind Talay's push for the role, saying they wanted to help him realise his coaching ambitions in New Zealand.
"We've talked to Uffy over the years about what his next step in his career was going to be, what he wants to do next," Dome told AAP.
"He said, 'I want to go on to bigger and better things and I want to coach internationally'.
"We said, 'In the past we've had the shared role with New Zealand Football, we said would that interest you if it came up?'. He said it would.
"So we'll put Uffy's name forward and it will be New Zealand Football's decision."
Talay is out of contract at season's end, and Dome said the club felt a split role could help them hold onto a coach who has taken Wellington into two finals campaigns in three COVID-dogged seasons.
"We rate Uffy very highly. We think he's a great coach. He's excellent with the players," Dome said.
"What he's achieved at Wellington Phoenix through some pretty extraordinary challenges over the last two years, I'm not sure too many coaches in the A-League could have done that."
Speaking after a 2-2 draw with Central Coast on Sunday, Talay said he had left the ball in the court of New Zealand Football (NZF).
"If anyone wants to talk to me they know where I am," he said.
A job share would be dependent on the A-Leagues continuing to pause for international windows, a practice that has been re-instated this season.
It has been done before, with Ricki Herbert overseeing the All Whites and New Zealand's sole professional club between 2006 and 2013, qualifying for the 2010 World Cup.
A number of backroom staff currently hold roles with NZF and Phoenix, including goalkeeping coach Jonathan Gould and under-age mentor Rory Fallon.
It is not yet known whether NZF want to go down that road again, or rate Talay as highly as the Phoenix do.
In 2019, NZF chose Hay over former Nix boss Des Buckingham, now in charge of Manchester City-aligned Mumbai City, who is likely to be considered strongly again should he have interest.
Underpinning Hay's dismissal is NZF's financial strife following their failure to qualify for the 2022 World Cup.
Qualifying will become easier for the 2026 tournament, with FIFA planning expansion to 48 teams and direct qualification for Oceania.
NZF, which has been approached for comment, is expected to formally open the position later this month.
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