The Scotland striker is currently under contract with the Vancouver Whitecaps until the summer of 2014, and McCoist has yet to hold any talks with the player.
Rangers remain under a transfer embargo and can recruit only free agents on September 1, and under the terms of Miller's contract with the MLS side, McCoist would not be able to sign him until January at the earliest.
But speaking after a 2-0 win over Berwick in the Ramsdens Cup, McCoist said: "Kenny 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 expects some of his players to depart the club before the current transfer window closes next week.
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."