The 17-year-old midfielder - who like Rogic blossomed with local club side Belconnen United - has reportedly agreed terms with the Hoops after catching the eye of coach Brendan Rodgers during a trial in November.
Mazis and Rogic share the same agents in former Reading and Socceroos defender Andy Bernal and UK-based lawyer Daniel Berman.
It was Canberra-based Bernal who introduced the youngster to Celtic, where Rogic - currently recovering from a knee injury - has forged a reputation for unorthodox excellence since his arrival back in 2013.
Mazis trialled alongside Canberra United's Nick Faust at Celtic's Lennoxtown training complex back in November where his pace, athleticism and promise prompted Rodgers to dangle the offer to join Rogic at Parkhead, according to the Scottish Sun newspaper.
Mazis posted a picture of himself and Kolo Toure on his Instagram account while in Scotland, with a dream deal now firmly in the offing.
Berman sounded a note of caution over suggestions a move would be concluded within two weeks, declaring: "It's somewhat premature to say that.
"If there is anything to announce then I am sure Celtic will do that in due course.
"Any exceptional young talent would be fortunate to sign and develop with such a great club."
Asked which aspects of Mazis's game brought him to Celtic's attention, Berman replied: "Leo's an exciting prospect who plays with a lot of confidence and he's also a tremendous athlete.
"He comes from a very supportive family and has been helped along the way by Andy Bernal, who of course has worked with Tom Rogic (during his formative years).
"He also has exceptional speed and technique and plays with bags of belief.
"He's also known for his stamina."
In addition to Australia, the rookie is also eligible, through his lineage, to play for Greece and Italy.
It's understood that the lure of the Azzurri is strong for him at this point, should they come calling.
Rogic, meanwhile, will return to Scotland from his brief Christmas break back home early next week to continue his recuperation from the minor knee injury which has sidelined him for nearly a month.
His last appearance was off the bench in the 1-0 UEFA Champions League loss to Anderlecht on December 6.
It's anticipated that if initial treatment has the desired effect the 25-year-old playmaker will swiftly resume light training with his teammates once back in Scotland.
Celtic are currently in Dubai at a warm weather training camp.
Eight points clear of Aberdeen at the top of the Scottish Premiership, they return to action from the winter break in the Scottish Cup at home to Brechin City on January 22.
Having played 27 games in all competitions, Rogic faces a "mini pre-season" to get back into match-ready condition as he bids to shrug off the nagging effects of knee inflammation which, at this point, is not considered to be anything more than a short-term issue.
With Australia locked in to face Norway in a World Cup warm-up against Norway in Oslo on March 24, and possibly Colombia during the same FIFA window, the yet-to-be selected successor to Ange Postecoglou will be hoping Rogic is fit and firing by then.
