Brown and Miller will see their sides come face to face in the semi-final
The Old Firm have been kept apart in the draw for the semi-finals of the Co-operative Insurance Cup.
Holders Rangers take on Motherwell, while Celtic will play Aberdeen for a place in the final.
Both ties are due to be played at Hampden Park in Glasgow on the weekend of the 29 and 30 January.
Rangers have already beaten the Fir Park side in the Scottish Premier League this season, winning 4-1 at Ibrox on 16 October.
The Glasgow side have gone 30 games without defeat against Motherwell, who have managed only eight draws since a 1-0 league win at Fir Park in December 2002.
Rangers won their last League Cup meeting, a quarter-final, 2-1 at the same venue in 2007.
If we win and get to the final, it will be great. Hopefully, I will be back and flying by then
Celtic captain Scott Brown
Celtic and Aberdeen have yet to meet this term, with the Dons due to travel to Glasgow on 6 November in the SPL.
Their last meeting was a thrilling 4-4 draw in February that ended Celtic's four-game winning streak in games between the sides.
They last met in the League Cup in the 2000 final, when Celtic won 2-0.
And Celtic captain Scott Brown is determined to help Celtic return to a Hampden final after missing out in both competitions last season following defeats by Hearts and Ross County.
The midfielder attended the draw still wearing protective footwear after breaking his metatarsal, but he is due to return weeks before the semi-finals take place on the weekend of January 29-30.
"Hopefully, the Old Firm will be the final match, but we will see what happens," Brown said.
"We have to try and go as far as possible in the tournament and, if we win and get to the final, it will be great. Hopefully, I will be back and flying by then."
Aberdeen director of football Willie Miller hopes the Dons will be in even better condition when the tie comes around after the return of Paul Hartley and Sone Aluko helped them reverse their recent form and beat Hibernian and Cup opponents Falkirk.
"It's an exciting prospect," Miller said. "We're pleased to be in the semi-final. Celtic are an exciting team and Neil Lennon is doing a fantastic job and we look forward to pitting ourselves against them.
"We have a lot of injuries just now and, if we can get players back, I'm sure we can make a game of it."
Motherwell face a team yet to be beaten in any competition this season, but midfielder Keith Lasley takes heart the good start made by Craig Brown's side themselves, who sit third in the league.
"I think it's been shown in the past, to win a cup you have to beat at least one side of the Old Firm at some stage," he said.
"We've got Rangers and we're really looking forward to it.
"And I think we've shown in the past, on the day, we can compete with the Old Firm. Everyone is going to be motivated and we believe we have the quality to do it on a one-off.
"Being on the weekend will make a big difference, we'll get more fans and there will be a bigger build-up. From a players' point of view, there is nothing better than playing at Hampden."
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