The Villains open up their campaign this evening with a trip to Bristol Rovers and McLeish has warned his players that they must be at their best to secure victory.
"It would be fantastic [to win the FA Cup with Villa]," he told ESPN. "It is a long time since we last won it, but this club has a great history and heritage in the competition and it would be nice to give the fans something to smile about with a cup run.
"But we have to go out there and give it our best tonight, we can't just expect to turn up and win."
Villa last won the FA Cup in 1957.