McCoist is keen to loan Gallacher out this season in order for him to gain further first-team experience.
The 24-year-old has played in all five of the Ibrox club's competitive matches so far in the 2013-14 campaign.
And the 6ft 2in shot-stopper has kept clean sheets in their last two games against Stranraer and Airdrie away from home.
But summer signing Cammy Bell is set to take over the No.1 spot against East Fife on Saturday and is likely to remain first choice.
McCoist, though, thinks Gallacher could represent a Scottish club in the top flight in the coming months.
And the Gers gaffer, who has had experienced English keeper Steve Simonsen on trial at Murray Park, confirmed clubs had been in touch.
He said: "Gall is doing really well. But we still feel it would benefit him and the team long term if he went and played somewhere for a year.
"I have got to say that looking at him he could play just about anywhere. He could certainly play in the top league in Scotland. I firmly believe that.
"The most important thing is that he goes out and plays and gets experience. There has been a little bit of interest in him, but unless we get another one in we can't allow him to go."
McCoist, who has also kept former Republic of Ireland youth player Sam Kelly in Glasgow on trial, has not given up hope of signing Bosnian centre-half Boris Pandza.
But he feels the club will have to reduce the size of their squad before the transfer window closes on August 31 before he can strengthen further.
He said: "I know Craig Mather has spoken to the agent. I haven't spoken to the player directly in three weeks, but we have spoken to the agent.
"We are very, very hopeful of getting something sorted. We need to get a bit of activity going the other way. It would probably help it if we did. There is interest there.
"The two boys who have been in on trial have looked good. The fact we are keeping them here for another week tells a story."
McCoist hopes Rangers can win their Ramsdens Cup match with Berwick Rangers tonight despite the fact he will be unable to play any trialists.
He said: "The players saw how well we played on Friday. If they want to get into the team and stay in the team then they will have to match that level of performance.
"We have got one or two lads who will come into the team tonight. They will have seen that game and seen how well they will have to perform to be involved in the future.
"We aren't getting carried away with Friday night. We played well for a spell in the second half.
"But we have set the benchmark. The players coming in know they have to perform to a certain level."