The Light Blues defeated Motherwell in the League Cup last season, before losing to Inverness and then crashing to defeat to Dundee United in the Scottish Cup.
But, rather than be apprehensive about the prospect of facing Scottish Premiership opposition again this time, Smith says McCoist would be keen to see how far his side has progressed.
Rangers host Airdrie in the third round, before the country's top teams enter the draw at the following stage.
Former boss Smith said: "I think Alistair would welcome a draw against a Premier division team for the simple reason that it would give him an indication of where his team are at the moment so that if there were adjustments to be made in the future he would have a better idea of what they need to be."
Rangers boast a 100 per cent record in the league so far, sitting eight points clear at the top of the table after eight games.
But Smith played down suggestions they could go through the entire season without losing a game in Scottish League One.
He said: "That's a hard task for any club to set out and say they are not going to lose a game.
"That's not football, it doesn't happen like that. On the field, Rangers have looked as though they have settled.
"The players are doing well for the club and they have been a better team to watch.
"They will strive to win every game. Whether they will do so or not remains to be seen."
One newspaper report this week claimed that an Ibrox director wanted McCoist sacked after Rangers crashed out of the League Cup to Forfar in August.
Smith said: "These are only media suggestions. I don't know whether that was the case.
"From a purely football point of view that would have been extremely harsh considering that in the League Cup this season they couldn't play any of their new players.
"Forfar is always a difficult place to go to and win anyway.
"We went there and got a tough Scottish Cup tie when I was in my latter stages as manager.
"I didn't think that was as surprising a result as a lot of people might have done when you take into consideration that Rangers couldn't play their new players.
"That would have been harsh but Alistair knows Rangers and when you lose a game like that you always come in for a bit of criticism and the spotlight is always on you."
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- Scottish Premiership