Celtic and Rangers are the two biggest clubs of Scotland and will compete with each other for the Scottish Premiership title next season.
Meanwhile, United are the biggest club of England and one of the biggest in the world.
Former Celtic midfielder Grant believes that only players coming from United would truly understand the pressure of playing for Rangers or the Bhoys.
The former Scotland international made the comments in reference to new Rangers midfielder Joey Barton recently making some bold remarks about Celtic midfielder Scott Brown and manager Brendan Rodgers.
The former Newcastle United and Queens Park Rangers man told talkSPORT at the weekend that Scotland international midfielder Brown is not in his league.
Barton also took a dig at new Celtic manager Brendan Rodgers, highlighting to The Mirror the fact that the former Liverpool and Swansea City boss has not won anything.
“The only people here who truly get what the pressure is like at Celtic or Rangers would be Manchester United players,” Grant told The Glasgow Evening Times. “They have a similar weight of being told they must win every game and win with a certain kind of style.”
Barton is a very good footballer, and even at the age of 33 remains a capable midfielder.
However, given the Englishman’s recent comments about Brown and Rodgers, he will be under immense pressure to perform well for Rangers next season.