Michael Fink, a 30-year-old German midfielder, has impressed on trial and his representative held talks with Charles Green, the club chief executive. David Templeton, the 23-year-old Hearts winger, is believed to be another the Rangers manager would like, having released defender Kirk Broadfoot from his contract.
"I would be really hopeful that we will get a few players in over the next 24 to 48 hours," said McCoist. "Between now and Friday is critical for the club for the next two years. Charles has a list of five who we would like. We need to get players in and of as high a quality as we can afford."
McCoist is hopeful Fink, a former Besiktas and Borussia Moenchengladbach player, will agree to commit his future to the club following talks over terms. "He has a pedigree. He has looked very comfortable in training. I would like to offer him something."
McCoist confirmed that Broadfoot had left amicably and praised his contribution over the past five seasons. "Kirk has agreed to have his contract made null and void," he said. "He is a great boy and a great lad. He has worked his socks off and he has never been a moment's bother.
"There was an indication we were forcing him out but that was never the case. It was Kirk's agent who mentioned it. There has been no fall-out and we, as a club, thank Kirk for his services and wish him all the best for the future."
McCoist, who is keen to hold on to Carlos Bocanegra, has signed seven new players but refused to use the influx as an excuse for another poor display in the 1-1 draw with Berwick Rangers on Sunday, instead insisting the players must put it right in their Scottish Communities Cup second round tie with Falkirk at Ibrox this evening.
"We were hopeless on Sunday, the performance was miles short," he conceded, "Our football content was poor and it must improve. It shouldn't be a culture shock going to these clubs as we're playing the same style of opponents. They are aggressive and in your face, but are also trying to play football as well. With the personnel we have, our team should be able to handle that. Dear me, we've got to be better than that.
"They had a wee pop at each other after the game on Sunday and that was good. I stood back and just kept a watch on it. Had they come in and not said anything I'd have been worried. I would have expected there to have been one or two voices heard in any dressing room with which I was involved as a player. It's important there are."
Alex Smith, Falkirk's technical director, believes the haranguing Rangers received after the Berwick match will act as a huge spur.
"The expected reaction from that game will probably not do us any favours as we will be up against a really motivated team out to show how much they were hurt. It makes the tie all the more difficult but we are still looking forward to it. If we can get our passing game going then we are in with a chance."