Steven Davis has given a heavy hint that he will be the latest Rangers player to sign a long-term contract.
It is believed that the 26-year-old midfielder is considering a five-year extension to his current deal, which has a year still to run.
Asked what stage negotiations had reached, the Northern Ireland international replied "still ongoing".
"I think it's just a matter of getting things sorted and hopefully getting things done and dusted," he said.
"I wouldn't put a timescale on it, but obviously I'm happy here, so hopefully we will get something sorted out."
McCoist appeared to believe Davis would be signing an extended contract when he explained the unusually long-term deals signed this week by goalkeeper Allan McGregor and defender Steven Whittaker.
"To be honest, the players asked for it and from where I was sitting it was a tremendous level of commitment to just about finish their careers at the club," said the manager.
"In my option, they have their best years ahead of them. So, from the club's point of view, it was a no-brainer.
"The three players have been part of the spine of the team in the last few seasons and, if you lose them, it is going to cost you a fortune to replace them."
Forward David Healy, utility man Andrew Little, left-back Sasa Papac and winger Salim Kerkar had already signed new one-year deals at Ibrox this summer.
And McCoist was confident that veteran defender and captain David Weir, who joined the squad as they headed for pre-season training in Germany, would follow suit.
"We are obviously talking to his representatives and hopefully Davie can stay for another year," he said.
McCoist head earlier expressed his delight at the retention of McGregor, who had been linked with clubs in England's top flight, and Whittaker, for whom Bursaspor had four transfer bids rejected.
"I'm thrilled that Allan and Steven have signed new deals with the club that keeps them with us for a long time," he told Rangers' website.
"There were clubs looking at both players and that was not a surprise because they are valuable assets to the club.
"It was well documented that Bursaspor were after Steven and there were one or two clubs sniffing about Allan, which is no surprise because he has been nothing short of sensational in the last few seasons."
Indeed, the man who has taken over Walter Smith spent time in South America over the summer checking on targets returned believing that he has an excellent core of players at Ibrox already.
"I was in Argentina over the summer watching about eight or nine games and I saw some good teams and some good players," added McCoist.
"But the best thing to come out of the trip was that it reinforced my belief that we have some very good players at this club.
"Sometimes you look about, but the grass is not always necessarily greener on the other side."