Although Smith's Ibrox contract expires in January, the 61-year-old has stated he will work without one if necessary.
"I don't know if he has had enough," McCoist said. "It is news to me that he withdrew his name; I didn't know that either.
"With his experience and what he did the first time, he would have to be at the top of any list that I would be picking as a supporter."
Smith has been priming McCoist as his replacement but the former Rangers striker laughed off suggestions he could speed up the succession by persuading his boss to return to Scotland.
McCoist said: "That would be far too scheming for me! I think the day is yet to come when Walter really listens to me to that extent.
"He makes his own mind up and he seems to be doing pretty well at that. I'll give him any advice he needs but I'm not sure he will be requiring it."
McCoist will not be putting himself forward to replace George Burley.
"No, I don't think I'll be doing that," he said. "However, it would be nice to be asked before you turn it down."
But he still sees the job as a "magical opportunity" for someone else.
"Obviously, it's a testing time for the national team," he said.
"Things haven't gone according to plan as George wanted. That goes without saying.
"Speaking as a supporter, it's high time we started to get back on a level keel because the last few games have been disappointing to say the least.
"I don't really go along with the theory that we don't have the players anymore.
"It goes without saying that we don't have a Souness or Dalglish but there are certainly good enough players in the squad to pick up."
Craig Levein quickly emerged as the favourite for the post but McCoist believes there are a string of worthy candidates, including Jim Jefferies, who brings his Kilmarnock team to Ibrox on Scottish Premier League duty on Saturday.
"Craig has done a great job at Dundee United," McCoist said. "Has he done a better job than Jim Jefferies at Kilmarnock? I don't know.
"These are the arguments the boys at the SFA will have to throw about.
"There are one or two contenders. Jimmy Calderwood did a good job at Aberdeen and is not in a job at the moment.
"I wouldn't go as far to say we're spoilt for choice but I would definitely say there are coaches and managers out there who the SFA will be looking at in the next few weeks and months."
McCoist added: "I think it's a job for someone to go and grab with both hands. What a magical opportunity it is for somebody."
Whoever the new manager is, he may be able to call on Rangers pair Allan McGregor and Kris Boyd, along with former Ibrox skipper Barry Ferguson.
Boyd withdrew his services to Burley after consistently being overlooked but stressed his decision was not final.
McGregor has already declared himself keen to return after SFA chief executive Gordon Smith revealed a new manager was free to pick him and Ferguson, who were banned for their behaviour during the World Cup qualifier against Iceland.
McCoist said: "From a personal point of view, as a Scotland supporter, I'm delighted because I want the best players to play for Scotland.
"I don't think we are particularly well off that we can knock back players that should be in the squad.
"I don't pick the squad and I certainly wouldn't envy the next man because it will be a difficult task.
"But, in that respect, I think he has got to have the option of picking the best players available to him.
"I don't think anyone could argue that Allan McGregor is not in the top two or three goalkeepers. Kris Boyd would certainly be in the top finishers. Barry Ferguson would certainly be in any Scotland squad on merit.
"So if these players are going to be available to the new manager, I can only think that's a great thing."