The Old Trafford club moved quickly to install interim manager Ole Gunnar Solskjaer on a permanent basis last month with the season reaching a critical stage.
The midfielder hopes Celtic might do similar in order to remove the uncertainty at the club and stressed current interim manager Neil Lennon is perfect for the permanent role.
“If you see the success with Solskjaer at Man Utd – people will ultimately judge you on success,” said McGregor.
“Obviously the club have to get the appointment right,” he added. “Whatever way they want to go about that and get it done but everyone around the club wants to know as soon as possible so you have the continuity going into next season. Whatever the board decides, as soon as the players find out it calms everyone down.
“It gives the club a focus. The new season comes pretty quickly.
“You only have three to four weeks off and then it’s straight back into the big games again. The sooner it is done the better for everyone.”
McGregor believes Lennon has already exhibited his qualities as Celtic manager, both during his first spell in charge and over the last eight games in his second stint.
“His track record at Celtic as a manager has been outstanding,” he said. “There’s not been many better in Europe and in league football as well. He has to have a case to get it.
“The transition since he has come in again has been excellent. He has the players hungry for success. It can easily peter away. But he has been great.
“He is a born winner as well and he’s bringing that out in the team. The stats and the performances, the results have been excellent.
“He has been proven here over his time before. He knows the fabric of the club and he knows everyone inside out. Not many people could have slotted in that well. It’s been a seamless transition for us.”
McGregor has only ever known what it’s like to be on top at Celtic since breaking into the team under Ronny Deila at the start of the 2014-15 season.
“If we get over the line it will be five [titles] out of five,” he said. “Coming through the academy here you have to be a winner. To succeed here you’ve got to win youth cups and everything like that. And if you get to the first team you have to succeed.”