New Zealand Rugby would not specifically confirm if Schmidt had been approached, but did say that the official process would be made public later on Monday.
Following Robertson’s exit, NZR chair David Kirk said the process to find his successor would see the appointment process opened up, and the net cast “far and wide”.
Current Highlanders coach Jamie Joseph and former Wallabies coach Dave Rennie have also been tipped as contenders for the role.
While Schmidt had also been tipped to take on a director of rugby role within NZR, overseeing national programmes for both the All Blacks and Black Ferns, appointing him as a head coach would also be a major coup.
Despite his 28 tests with the Wallabies returning just 11 wins, Schmidt’s tenure has seen him forced to rebuild Australia’s national side, after the turmoil caused when Rennie was sacked to appoint Eddie Jones - who in turn left to join Japan after the 2023 World Cup.
As Ireland head coach, Schmidt helped turn the perennial underperformers into one of the best sides in the game, winning 55 out of 76 tests - including beating the All Blacks for the first time in 2016, and again in 2018.
When NZR made the decision to sack John Plumtree and Brad Mooar in 2022, Schmidt was parachuted in to assist Ian Foster, and in turn helped turn the All Blacks into the side that reached the final of the 2023 World Cup, and lost to the Springboks in the final by one point.
Schmidt’s tenure with Australia has continued to be extended the longer he’s remained with the Wallabies.
While he was initially contracted through to the end of last year’s British and Irish Lions Tour, that was extended to the end of 2025, and then again to mid-2026 to aid his successor.