The 33-year-old underwent a trial with the Gunners as a teenager in 2005 but the club elected not to make his move permanent.
Redmayne was the star of the show as the Socceroos secured qualification to the 2022 FIFA World Cup after a thrilling penalty shootout victory over Peru in the playoffs.
The Sydney FC goalkeeper is considered a penalty specialist and was brought in the dying minutes of extra-time and went on to make the crucial save that fired his nation to a sixth FIFA World Cup appearance.
Wenger was full of praise for his performance and stated that Arsenal passed up on the opportunity to sign him in 2005.
"If he was with us, we made a mistake.
"At the end of the day, I would say their [Australia] goalkeeper was man of the match."
Australia booked their spot in the AFC FIFA World Cup playoffs by finishing third in Group B.
They secured a 2-1 victory over the UAE in the continental playoffs to progress to the intercontinental playoff against South American side Peru.
The two sides could not be separated in a goalless draw after 120 minutes of action and proceeded to penalties. The Australians eventually prevailed in a 5-4 victory to secure qualification for a fifth successive World Cup.
They will square off against France, Denmark and Tunisia in Group D and will attempt to progress to the knockout rounds after three consecutive group stage eliminations in the competition.
Andrew Redmayne is the latest in a long list of players who were on Arsenal's radar as youngsters
Arsenal have an extensive scouting system that recognizes highly talented players at a young age. Most of these players undergo trials with the club's academies before going on to achieve superstardom elsewhere.
A list of players who were on the Gunners' radar as youngsters but were not signed includes some of the greatest players in recent history.
Arsene Wenger has revealed that the club identified the talents of Zlatan Ibrahimovic, Cristiano Ronaldo, Lionel Messi and Kylian Mbappe but passed on the opportunity to sign them.
All these players have gone on to become all-time greats, but the story might have been different if Arsenal had solidified interest in them when they were younger.