Ajax have told Manchester United they will not be able to sign Daley Blind on the cheap.
Wolves manager Kenny Jackett has admitted to being among those to have enquired as to Patrick Bamford's availability.
The Light Blues boss is keen to bolster his defence and the Bosnia-Herzegovina international remains on the radar.
The 26-year-old centre-back has been the subject of protracted talks stretching back a number of weeks, and McCoist says the player is still on his wanted list.
He said: "Not all transfers are clear-cut and can get done in 24 hours.
"This one is obviously taking a little bit of time but I would still be very hopeful.
"My job as manager is to improve the squad where and when I can.
"There are one or two players I would like to bring in so we will see over the next few days if we can get them in.
"I would like another centre-back and I would like to get another forward as well because I think we are a little bit sparse in those areas in terms of injury and suspension."
McCoist also wants to add another goalkeeper to challenge Cammy Bell for the gloves.
Steve Simonsen has been training with the squad, along with former Everton midfielder Sam Kelly.
"Both of them are here for another week," McCoist said.
"The fact that they're back for another week would indicate they are doing well and we're happy to have them for another week.
"In terms of offering something longer term, it will probably be Thursday or Friday before we know any more on that."
Rangers head into the Ramsdens Cup second round tie against Berwick Rangers on a high following Friday's 6-0 thrashing of Airdrie in the Scottish League One on Friday.
McCoist said: "If I could get a repeat of Friday's game, I would be delighted.
"Berwick have posed us one or two problems in the past and they have started the season reasonably well.
"We go back to last year's side in the respect that we can't play any of our new faces.
"It's a game we are looking forward to after a good performance and result against Airdrieonians but we will have to be very careful as well."
Rangers must wait until September 1, when a transfer embargo is lifted, to register their eight new players.
Competition rules restrict them from fielding trialists beyond the first round of the Ramsdens Cup so Jon Daly and Nicky Law - both on the scoresheet at Airdrie - are ineligible for the visit of the Wee Rangers.
McCoist added: "I've got one or two concerns, but there is nothing I can do about it.
"We just have to go out and prepare right, which we attempt to do for every game, and treat the opposition with respect.
"It's up to the boys who go out and play the game (on Tuesday) night.
"We are expected to do our best - and we expect to do our best - in every competition we are in and give everything we've got.
"The Ramsdens Cup is no different. Queen of the South put us out last year and we want to do well in the competition this year.
"We want to go all the way. It's no different from any other competition.
"It's not ideal because of the circumstances in terms of the personnel we are allowed to pick from.
"But that's where we are and we just have to get on with it."