Bell is one of a number of players who have been targeted by the Light Blues as they seek to strengthen for next season.
However, McCoist looks set to face competition for the Rugby Park number one after Killie boss Kenny Shiels revealed Ipswich are one of several English sides interested.
Rangers are currently under a transfer embargo and must wait until September 1 before they can register new players, who must be free agents.
McCoist said: "I haven't spoken to Cammy myself but I believe there have been discussions with Cammy's agent.
"How far down the line they are remains to be seen.
"Players like Cammy do automatically fit the bill because they are out of contract.
"Hopefully there are players who are within our remit who we can go and sign.
"I wouldn't like to name individual players but certainly we are looking at a large number of players who we can hopefully bring in this summer with the view to registering them on September 1.
"The fans have been fantastic and I think what they deserve is a little bit of freshness coming into the squad, if we can give them it.
"They obviously know about the transfer embargo and our hands being tied.
"But we will try to give them an improvement on what we had and what we've got this year. That's our job and we intend to do it."
Asked if his Irn-Bru Third Division side can still compete with npower Championship clubs like Ipswich, McCoist said: "Time will tell.
"We are certainly in a far weaker position than we've ever been in terms of bringing players to the club.
"I've had players telling me they would love to come in normal circumstances but declined the offer due to where we are.
"In terms of our pulling power to sign players, it's as weak as it's ever been."
Thursday marked one year since Rangers were forced to call in the administrators, after HMRC lodged a petition over the non-payment of PAYE and VAT since Craig Whyte's 2011 takeover.
Liquidation was confirmed in the summer and the club was forced to start from scratch in the bottom tier.
Whyte appeared on television on Thursday, when he denied being a crook while claiming he slept soundly at night after refuting any suggestions of wrong-doing during his stewardship.
McCoist, who did not watch the interview with the former owner, said: "Well, I must admit, in the last nine months or so, I would have enjoyed the luxury of sleeping at night - that's for sure.
"I certainly didn't sleep particularly well, as was the case for all the staff here and probably the vast majority of fans.
"So I'm pleased somebody is getting a good sleep at night.
"The good thing is, we are getting a lot better sleep now because of the platform we have."
Asked if he was annoyed by Whyte's comments, the Gers boss said: "If you thought about it greatly and dissected it and listened to everything and took all the points, there are probably things that would disappoint and annoy you.
"But I'm refusing to do that until all the truth is out. Then I'll have a look at the whole thing.
"I don't think there is any point in me, personally, looking back now and getting angry and disappointed.
"It's my job to look to the future and build for the future and that's what I intend to do."
Rangers return to Broadwood on Saturday to face a Clyde side who provided their first away win in the league this season, having initially struggled to adapt to games on the road in the Third Division.
McCoist said: "It was a really important step for us, that particular game, because we had three games which we had drawn and one was a defeat at Stirling.
"People were, rightly, questioning the results away from home. So it was a big, big step for us. It will be equally difficult tomorrow."
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