Miller, who has scored 20 goals for Rangers this season, has rejected the club's latest offer and could leave for nothing at the end of the season.
However, despite Rangers' financial problems, Bain sees no logic in selling the 31-year-old.
"My stance on selling in January - and I am sure that Walter's is the same - is that the squad is weak in terms of number and in depth," Bain said.
"We are going to need everybody we can to win the championship and Kenny is going to be a big part of that.
"I don't see Kenny going anywhere in January. It's in my hands to say we are not selling Kenny."
Bain has not ruled out a deal being struck, although he has been "back and forth several times" to the former Celtic player's agent.
The Rangers chief executive praised Miller for remaining focused despite the uncertainty.
"From a club view, we have to look at the correct governance, the age of players and the length of contracts they want and the amount of money he wishes to be paid," Bain added.
"Then, he is a player on form delivering goals. I've certain targets I have to meet within a business plan, so there is a bit of a juggling act."
With tycoon Craig Whyte still weighing up a takeover deal, Miller could yet secure the deal he is looking for in the long run.
And Bain is "very, very positive" about the prospect of the in-form Steven Naismith extending his stay.
"He's been offered a four-and-a-half year contract," said Bain, who will also open talks with defender Sasa Papac soon.