Gauci, 23, is the only Socceroo in the Premier League, having signed with Villa from Adelaide United during the transfer window.
After Australia were knocked out of the Asian Cup, Gauci - who didn't make an appearance at the tournament - flew out of Doha in the early hours of Saturday.
He will have all of two days back in Adelaide to pack up his life before heading to Birmingham.
Gauci's eyes lit up, though, at the thought of working alongside Martinez.
Captain Mat Ryan remains the man in possession of the No.1 jersey for Australia. (Dan Himbrechts/AAP PHOTOS)
The 31-year-old famously went from slugging it out as Arsenal's reserve goalkeeper to Aston Villa's star shot-stopper - and then golden glove winner in Argentina's 2022 World Cup triumph.
"It's going to be really something special having someone of that experience (alongside me)," Gauci said.
'He's had to wait for his opportunity to be a No.1, but he's taken it with both hands and ... his last 24 months have been phenomenal.
"Everything that he's done, he's playing at a really high level with both club and country.
"So to see how he works from the day to day and the output on the park and off the park, it's going to be amazing.
"It's the Premier League at the end of the day, and these are world-class players. The things that they do from day to day are going to be amazing to see.
"I'm really eager to listen and learn."
Villa sit fourth in the Premier League and are still in the UEFA Conference League and FA Cup.
Gauci will be playing alongside Villa's World Cup golden glove winner Emiliano Martinez (right). (EPA PHOTO)
Gauci indicated he wouldn't be going out on loan, instead developing at Villa where he will work alongside Martinez and Swedish veteran Robin Olsen as he waits for his breakthrough.
"Playing games is extremely important, but also this is an opportunity to take my career and develop myself as a goalkeeper and take that to the next level," he said.
Gauci grew up idolising former Brighton & Hove Albion and Arsenal EPL goalkeeper Ryan, who has had a stranglehold on the national No.1 jersey for a decade.
Now the 194cm South Australian, with two caps to his name, is coming for Ryan's spot.
"Maty's been Australia's No.1 for a long time, but of course I'm pushing," Gauci said.
"I want to push, I want to play, I want to play games.
"I've had a taste of it in Ecuador last March and then the Bahrain game in the lead-up to (the Asian Cup).
"Every opportunity that I get to put on the shirt is a great honour.
"Of course I want to push Maty - and he wants me to push him as well. At the end of the day, it's healthy competition.
"I'll wait for the opportunity, but first and foremost, it's about what I'm doing at club level.
"That's what will get me there."
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