The Scotland striker, who has scored 20 goals for Rangers so far this season, sees his current deal expire at the end of this season and will be free to talk to potential suitors next month. It is understood an offer of a one-year extension from Rangers remains on the table for Miller, the 30-year-old having earlier rejected a two-year offer which would have seen his salary related to performance in the second year.
Ibrox chief executive Martin Bain explained: "I made Kenny an offer after many positive discussions with his agent Dave Baldwin, who is fine to deal with, and they have not liked the most recent offer. That's where we stand. I am not the type to be obstinate and entrenched, but we have been back and forth many times. I really do value Kenny, as does Walter Smith, and we want him to stay. At the end of the day, budgets come into it and that is where we are.
"I understand Kenny's situation. But from the club's point of view, we have to look at the player's age, the length of contract he wants and the amount of money he wishes to be paid."
Regardless of the contract stand-off, Bain insists Miller will not be sold during the January transfer window. "My stance on that, and Walter's is the same, is that the squad is weak in terms of numbers and depth," added Bain. "We are going to need everyone we can to try and win the championship and Kenny is going to be a big part of that. It's in my hands to say we are not selling Kenny and I don't see him going anywhere in January."
Bain also confirmed he expects in-form midfielder Steven Naismith to agree a new contract with Rangers imminently and is also planning talks with full-back Sasa Papac who, like Miller, will be a free agent next summer. "I am very positive about Steven extending his contract," said Bain. "He has been offered a four-and-a-half year deal. As for Sasa, I was going to sit down with him in Turkey last week but he didn't travel. The only reason I haven't spoken to him so far is that he doesn't knock on my door or pick up the phone like half of the others do. He is such a lovely lad and when you are so nice, people probably take advantage of you. But I am going to sit down with him in the next week or 10 days."
• The SPL has announced new dates for the Celtic v Kilmarnock and Hamilton v Hibernian matches postponed at the weekend due to the weather. Celtic's rescheduled match will take place at 7.45pm on Tuesday, 21 December, with the Hamilton v Hibs game 24 hours later. St Mirren's home match with Kilmarnock, scheduled for New Year's Day has been moved to 3pm on Monday, 3 January.