Miller predicted the Hoops would complete their comeback to wrest the title back from Ibrox.
"I don't think it's too big a gap," he said. "There have been gaps in previous seasons which Rangers and Celtic have clawed back.
"It was a 10-point gap last week and now it has been reduced to eight.
"Celtic are going to keep pinching away at Rangers hoping that they will drop points and they dropped points against Motherwell on Wednesday.
"It's all down to confidence and who has the best run-in between now and the end of the season.
"But I think it will go to the last game of the season - and it will go to Celtic.
"Over the January window, you saw quite a few changes at Celtic and Tony has brought his type of player in so between now and the end of the season, you are going to see a different Celtic team.
"In the game against Hearts they showed glimpses that they are going to be exciting to watch and good on the break.
"There are players who can open up defences and that is the sign of things to come."
Miller is impressed by the fledgling partnership of Keane and Marc-Antoine Fortune, who scored the clincher against the Gorgie side to take his tally for the season to nine.
The former Clyde boss said: "Marc-Antoine Fortune had a nervous start but he is starting to progress now.
"Tony has put in a certain style of play and the addition of Robbie Keane has helped as well.
"Keane is going to open up quite a few defences, he plays on the shoulders of defenders and runs in behind people.
"When you play for Celtic or Rangers, they are always going to create chances.
"Robbie and Marco will get chances, it's up to them to put them away.
"Robbie got a few chances against Hearts and got a bit frustrated that he missed them but he got in to the positions and I'm sure that once he sticks one or two away he will have a good tally at the end of the season."
Miller, who had two spells as an Aberdeen player either side of his time at Parkhead, believes the Dons are unlikely to finish much higher than their current sixth place but after gaining a point against Hibernian at Easter Road on Wednesday night, he expects them to make things tough for Celtic on Saturday lunchtime.
"Mark McGhee has been chasing third spot and he will be looking for Hibs and Dundee United to slip up," he said.
"I don't know if it is a realistic target, I think a top six position is but they have to keep plugging away and hope teams drop points.
"After a tough game against Raith Rovers, they responded well against Hibs and showed there is a good spirit among the squad and Mark will be looking for them to continue that against Celtic."