Hateley saw first hand how much of a threat his former strike partner posed against the Hoops as a player.
And he believes McCoist will be far from daunted by the experience of heading into the famous fixture as a rookie boss.
Hateley said: "It's always nice to get the monkey off your back.
"Alistair is no different. He stood up against Celtic as a player and he still stands up as a manager.
"His results this season speak volumes for him already.
"They dropped a point at the start of the season but it's the only goal they have conceded in the league."
Several players could be handed their Old Firm debuts this weekend and Hateley jokingly offered his advice to those experiencing the match for the first time.
"Put your hard hat on and keep your head down," he said.
"They are great games to play in. The guys who are making their debuts, the likes of (Carlos) Bocanegra and (Dorin) Goian, they are experienced players.
"They have plenty of caps between them and they have been around the block.
"This is unique but all that experience they have got will stand them in good stead."
Hateley expects striker Nikica Jelavic - who netted the winner against Celtic in the League Cup final - to have a big part to play.
The Croatian was the subject of a transfer deadline day bid in the region of £9million from an unnamed club and Hateley says this game is a chance for Jelavic to show that remaining at Ibrox is not a problem.
The former Gers forward said: "I think his head was probably slightly turned on transfer deadline day by the bid that came in for him from a huge club.
"It's now all about getting him back on track. What they will be looking at now is a reaction to the disappointment of not getting that move but I would suggest he is a person who is a team person.
"He's a worker - he's not one of those guys who will mope around. I think he will get on with it and do what he does - play well and score goals."