Scottish Premiership table-toppers Aberdeen host Celtic at Pittodrie on Saturday in what is a crucial barometer of how far Derek McInnes's Dons have progressed.
Gothenburg Great Miller is convinced the team can push for a second-place finish for the first time since he was Dons manager 20 years ago.
And beating Celtic this weekend would signal "good times ahead" for Aberdeen, according to Miller's former central defensive partner and fellow ECWC winner McLeish.
Former Dons skipper, manager, and director of football Willie Miller believes the signs are there that Aberdeen can push Celtic all the way this term.
Miller told the Scottish Daily Express: “It was a very impressive result for Aberdeen to win 3-1 away to Motherwell.
“It will give them a lot of confidence coming on the back of the impressive home victory over Kilmarnock on the opening day of the season. But to win down at Fir Park is a better gauge as to where they are.
“It has certainly reinforced my opinion that this should be a good season for the Dons.
“The squad looks strong enough to maintain the challenge this season, but we will find out even more when they face Celtic.”
Meanwhile, Alex McLeish told BBC Sportsound that the Dons should be brimming with confidence ahead of Saturday's Pittodrie encounter.
"Let's see how far they've come and judge them on that one," he said.
"There's always been fantastic potential at Aberdeen, despite the many years without success.
"They've got off to a flier and it will have given them amazing confidence to have won those two games.
"Going away to Motherwell, the form team of last season, and winning 3-1, is an enormous boost for Aberdeen. Derek McInnes has got them flying."