Aberdeen and Celtic played out a thrilling 3-3 draw at Pittodrie last weekend, with the home side scoring a late equaliser to deny the Scottish champions all three points.
Celtic managed to earn a point from their trip to Lille on Thursday night and are coming into the game on the back of gaining some confidence from their French adventure following a poor run domestically.
McManus believes Aberdeen will fancy their chances against Celtic, but it will depend on how the players manage to handle the occasion on Sunday.
However, he McManus admits that Celtic have a terrific record in cup games and have looked impregnable at Hampden Park in recent years.
The former forward believes that it will be a competitive game, but feels Celtic will eventually edge it.
McManus said on PLZ Soccer: “They [Aberdeen] will fancy their chances.
“There was nothing in it last week and I felt Aberdeen deserved the draw.
“So [it is] if they can go there and handle the big occasion and the big pitch, as Celtic have a phenomenal record at Hampden.
“I could not tell you the last time they lost a game there. 34 games in a row they have won in the cup and so they are a hard team to beat in the cups.
“And I think Celtic will just edge it, maybe after extra time.
“I think it might be to two each and Celtic might nick it in extra time.”
Celtic have won their last seven matches against Aberdeen at Hampden Park.
Their last defeat against the Dons came in the Scottish League Cup semi-final in the 1992/93 season.
