The Ibrox club has tabled an offer for the former Hearts and Celtic forward, who has been training at
The Rangers boss faces a race against time to assemble a squad before a 12-month transfer embargo comes into effect on 1
And he hopes to add Beattie to his list of captures after recruiting
McCoist told rangers.co.uk: "I have meetings with (chief scout)
"We will push a few names forward and see where we go.
"Charles has spoken to
"As yet, I have not heard back from him or from Craig but hopefully I will do in the next 24 hours."
McCoist is also hopeful of retaining the services of defenders
A number of other first-team regulars refused to transfer their contracts to the Rangers newco and have since sealed moves elsewhere.
McCoist added: "As far as I know, both Carlos and Dorin are staying.
"We don't want to lose the spine of the team and those two centre-backs make up a great part of our team so hopefully they will remain with us."
Shiels claims he turned down offers from clubs in
The former Kilmarnock midfielder has agreed a four-year deal.
Shiels is the second player to sign for the Glasgow giant since it was consigned to liquidation in the northern summer, and voted into the Third Division, after Black's capture at the weekend.
Despite being demoted to the bottom tier of the Scottish Football League, Shiels insists the offer from Rangers was still the most attractive on the table.
He said: "There were moves to England and abroad but none were the size of club that Rangers are.
"The important thing in my decision as well was, playing against Rangers, you see the size of the club and you see the fan base that they have.
"The fans are a massive factor in this club. What sticks in my head was when Kilmarnock beat them 1-0 last season and it had just come out that Rangers were going into administration.
"I've never seen an atmosphere like it that day.
"The Rangers fans were bouncing throughout the 90 minutes and that shows the enormous size of the club and the enormous support that they have.
"There has been interest for a while now. Knowing I was wanted, a few months ago, when they were still in the SPL, was a good factor.
"I felt wanted and I was keen to come here. As soon as I spoke to the manager, my mind was made up."
When put to Shiels that some may question his ambition by joining a Third Division club, he replied: "I don't care.
"There are going to be critics and people will give their opinions but I've made a decision for myself and for my family and I'm delighted to be here.
"I see it as a challenge, as a personal challenge, to try to do my bit to get this club back to where it belongs, back to top-flight football.
"First and foremost, I wanted to sign for Rangers. No matter what league they are in, it's a massive club.
"I can't wait to get started. I'm delighted to be here, it's one of the biggest clubs in the world.
"I feel as though my best years are in the next four years and I want to give them to this club."
William Hill has extended its sponsorship of the Scottish Cup for a further two years.