The Australia star has nailed four goals in five league starts for new club Hertha Berlin, and the 26-year-old's purple patch has set tongues wagging across Germany.
Not least among two of the game's royalty, former Germany captain Matthaus - his nation's most capped player with 150 appearances and a 1990 FIFA World Cup winner - and his 71-cap former teammate Ziege.
The trio have a common link, all having represented Borussia Monchengladbach at various points of their careers.
Matthaus, now a leading German TV pundit at the age of 56, and former Liverpool and Tottenham wing-back Ziege, 45, are delighting in Leckie's Bundesliga goal burst and electric all-round form.
"He's clearly Hertha's best signing of the pre-season and has been superb for them in everything he's done so far," Matthaus told The World Game.
"The way he's playing, and the confidence he's showing, he could go on to become possibly the signing of year across the competition.
"It's early to say that yet of course, but if he keeps up the consistency, and just as importantly the goal threat, then he can have an incredible year.
"He's not been known as a goalscorer in the past, and that's been a huge addition for him."
Ziege, who put his hand up for Adelaide United coaching job before it went to compatriot Marco Kurz, is equally effusive over Leckie's storming start to life for eighth-placed Hertha following his arrival from relegated Ingolstadt.
"I've been watching his career unfold and flourish for a few years now," said Ziege, Gladbach's one-time interim coach and director of football.
"I agree he can become one of the best transfers of the season if he carries on like this.
"I've always liked him as a player ... his strength, pace and energy have always been there.
"But he also has very good technique and a football brain.
"He's playing in a more advanced position for Hertha than he did for Ingolstadt last season (where he remained goalless after 30 league games), and he seems to be thriving.
"He's also scoring quality goals ... and that can only come when the confidence is high.
"He scares defenders with his speed and if Hertha are going to push for one of the European places this season, he can be a big part of that."
Leckie will be looking to continue his streak when Hertha, who have picked up eight points from their opening five games, visit struggling Mainz 05 on Sunday (AEST).
As if blessed by a goalscoring epiphany, Leckie is making up for lost time after netting just 10 in three previous seasons at Ingolstadt.
The run could have positive ramifications for the Socceroos ahead of next month's 2018 FIFA World Cup play-off against Syria, and might provide coach Ange Postecoglou further encouragement to revert from a 3-2-4-1 formation, which effectively dulls Leckie's attacking instincts, to a 4-3-3 to give him full rein.
"What we're seeing from him now has been coming for a while ... and I'm just sitting back and enjoying watching him do his thing," said Matthaus.