Celtic will take on Kilbride away from home at the K-Park Training Academy in the fifth round of the Scottish Cup on Sunday afternoon.
The Scottish Premiership giants will head into the game as favourites, and former Celtic midfielder Hay has predicted the Glasgow giants to get the better of the Lowland Football League outfit.
“No disrespect to East Kilbride at all, but this is a game where Celtic should go out and run over the top of them,” Hay wrote in The Glasgow Evening Times.
“The game comes on the back of what has been a difficult week, but it has to be a measured and strong performance against the Lowland League team.”
“It has to be straightforward and efficient, and the only way for them to quiet the noise around the club now is to go out and win games,” added the former Celtic manager.
Celtic will head into the game on the back of a 2-1 defeat to Aberdeen away from home in the Scottish Premiership.
It followed a 3-1 loss to Ross County at Hampden Park in Glasgow in the semi-finals of the Scottish League Cup.
It has been a tough few days for Celtic manager Ronny Deila, who will want his players to step up and register a big win in the Scottish Cup this weekend.