McGhee is sure Ibrox manager Walter Smith will lift his players for Saturday's lunchtime kick-off at Pittodrie but feels his own side are now in their best shape of the season after beating St Johnstone and drawing at Motherwell in their previous two fixtures.
"Walter Smith has been there and done it and he knows how to galvanise his troops," said McGhee.
"He will have left that behind and will be looking forward now to retaining the championship and making sure they're in the Champions League next year.
"That's all he can do now so he will be fully focused on that.
"We can't expect any favours because of a bad result they had in midweek.
"Whenever you play the Old Firm it's always difficult for the rest of us.
"I think we're getting them at a good time in the sense of ourselves.
"I think we're in as good shape, in terms of mentally in particular, going into this game as we have been all season.
"We have a team selected that we think can do the business against Rangers. But that's because of us, not them."
However, McGhee admits his side have to be more clinical than they have been in recent weeks.
"One of the things that happened in both those games was that we made a lot of chances," he said.
"We're making good, good chances. I'm not talking about opportunities to make chances, I'm talking about clear-cut chances.
"If we make those sort of chances against Rangers, we're going to have to take a couple of them to win."
Meanwhile, McGhee has still to follow up his interest in Aberdeen-born USA international midfielder Stuart Holden.
McGhee has been tracking the Houston Dynamo player since he was Motherwell boss.
"The reports are saying he's possibly prepared to come back to the UK," McGhee said.
"So far we have not made any inroads into contacting his representative or the boy himself.
"All I can say is he is a player we would be interested in. He is a player that is on our list, as are others, but I don't know if there is any possibility of us bringing him in."
McGhee has been continuing his bid to secure his present squad on longer contracts and held talks with the agent who represents Lee Miller, Gary McDonald and Mark Kerr on Thursday.
"We have told him what we think and now he will report back to his players," McGhee said. "I'm hopeful, it was a positive meeting."
Rangers 4/5, Draw 13/5, Aberdeen 10/3