The Rangers boss says no deals are imminent but he continues to monitor the trialists who have been part of his squad at Auchenhowie recently.
With Maurice Edu seemingly set to complete a move to Stoke City, Rangers have been linked with a number of players including Morgaro Gomis and Daniel Larsson.
However McCoist refuses to discuss individual targets.
He said: “We haven’t had any dealings with Gomis’ club. He’s a player that we like but it would be unfair of me to speak about individuals at the moment.
“Daniel is a good player and someone who played well against us last year in Europe.
“He’s somebody else’s player at the moment and although he’s a good player I wouldn’t like to comment on somebody else’s player.”
McCoist spent much of today’s training session on his phone and admits that’s likely to continue as he looks to get players in during the coming week.
He added: “That’s been the case for a few days and it will probably be the case for the next few days.
“We’re hopeful that we can certainly get four or five anyway over the line before the window closes.
“There are no signings really imminent at the moment, but certainly the wheels are in motion on three or four targets.
“We’re still monitoring the trialists and they’ll be here for another three or four days most of them.
“Again I think there is probably one or two coming in over the weekend so we’re in a position where we’ll keep monitoring and if anyone impresses we’ll be in a position to offer them something.”
McCoist says it hasn’t been difficult to convince players to join his squad, despite the club’s drop to the fourth tier of Scottish football.
He said: “It’s not as hard as you might think. The only down side is that you’re not playing in the top level.
“I wouldn’t imagine there are too many clubs that can provide 50,000 fans for an SFL game, or a training facility such as this, that competes with anything in Europe.
“The club is still the club, it’s the same football club, the same stadium, the same environment to train in.
“The down side is that players do generally want to play at the top level, but up to now we’ve been fortunate in the players that we’ve signed because they have been SPL players and very good ones at that.”