The Dons are looking to wrap up a famous hat-trick of wins against Celtic by beating the champions at Parkhead today, ahead of their final two fixtures with Dundee United and Motherwell next week.
They lead Stuart McCall's Fir Park side by four points in the race to finish runners-up to the Hoops.
But former Celtic midfielder McGinn insists the League Cup winners have already proved this season that they have the bottle to handle pressure situations, and he insists they will be fearless as they take on Neil Lennon's team.
The Pittodrie outfit's 13-goal top scorer said: "Celtic are coming off the back of last week's performance when they beat Inverness 6-0 and they will want to get near to that 100-point mark.
"But we are at the stage now where we don't fear anyone. We want to push on and finish second. It's exciting times for the club and we have nothing to fear down there at Celtic."