The Light Blues boss has yet to hold talks with the veteran striker, but says he is keen to explore the possibility of a possible return to Glasgow.
Miller recently signed a new deal with Vancouver Whitecaps which keeps him at the club until summer 2014.
That means Rangers - who are under a transfer embargo and can only register free agents on September 1 - would have to wait until January at the earliest to sign the 33-year-old.
Speaking after a 2-0 win over Berwick in the Ramsdens Cup, McCoist said: "He would certainly interest me, I would be lying if I said he didn't interest me quite a lot.
"If there was an opportunity to get Kenny, I wouldn't be doing my job if I didn't explore that. We will have to wait and see.
"I keep in touch with Kenny, but I haven't spoken to him since the day after the England game.
"In terms of the possibility of him coming here, I haven't spoken to him about that.
"I wouldn't rule it out. I'll certainly be making enquiries in the next wee while.
"If it's a possibility, it's an avenue we would look to possibly pursue.
"I don't know if Kenny would want to come, if we could afford him. There are millions of questions but I do think we need another forward."
McCoist also confirmed some players could seal their exits from the club in the current transfer window.
He added: "That's a possibility. There have been one or two enquiries made about one or two of our players.
"But it would be unfair of me to mention them because the players don't know yet and it's miles away from anything concrete happening."
Goals from Barrie McKay and Andy Little secured victory over Berwick and McCoist said: "I thought it was a solid performance and a well-deserved win."