The midfielder has not featured in either of the two games since McLeish took charge of The Reds.
But the new manager is toying with the idea of making the most of the opportunity to take a closer look at more of the players he has inherited, among them Gillett.
“I know the quality of Simon Gillett,” he told Forest Player. “He’s great on the ball and has a habit of keeping it which is obviously a fantastic quality to have.
“He’s not featured yet in the two games so perhaps we’ll look at Simon.
“And without wanting to name the team just yet, there are perhaps one or two others that might come into contention.”
Forest are overwhelming favourites to overcome League One strugglers Oldham and clinch a place in the fourth round draw but McLeish is taking nothing for granted.
“I love the FA Cup – it has a magical history,” he says. “Whenever it comes around everyone perks up and loves the drama it provides, the giant-killings and surprises.
“But we hope that we can progress as far as we possibly can.
“We must give Oldham the utmost respect, play to our absolute maximum and not go into the game with any complacency. Then we will have a good chance of winning.”