Wigan want to play against Australia when they tour the UK next autumn.
Kangaroos coach Mal Meninga hopes to revive the midweek matches when they tour next season to play England in a three Test series.
And the Warriors hope to prolong their 2020 season by taking on the World Champions - like they last did in 1994.
"Wigan would love to play the Kangaroos," the club's executive director Kris Radlinski told the NRL website. "One of the highlights of my youth was watching Wigan play the 'Invincibles' in 1982 and 1986."
Details of England's three-Test series against Australia in 2020 - a year before the World Cup - are expected to be confirmed later this month.
They are unlikely to include any midweek fixtures, as they have not been finalised, but Meninga is keen to revive the idea of playing leading Super League clubs in between the Tests.
The former Australia captain said: "We have got three Test matches against England and hopefully some mid-week games against the clubs over there or maybe France."
Meninga played in the Kangaroos side which beat Wigan 30-20 in front of 20,000-plus fans at Central Park in 1994.
The tradition was abandoned when the British season switched from winter to summer for the start of Super League in 1996.
A Wigan-Australia match would generate a lot of interest, and revenue, but it would mean prolonging their season until at least the end of October, when the players are usually on their off-season break.
It would also throw up the strange prospect of Adrian Lam coaching against Australia, even though he is Meninga's assistant with the Kangaroos.
Wigan could also play an early-season match against Canberra in early 2020, possibly on the same weekend as the World Club Challenge in February.