Moyes will officially take over at United on 1 July after agreeing to succeed fellow Scot Sir Alex Ferguson, who will bring an end to his hugely successful 26-year reign as manager on Sunday.
And Ferdinand, 34, believes reputations will count for nothing in the eyes of the new boss.
"We've got to prove ourselves to the new manager," Ferdinand told MUTV. "He's going to come in with new ideas, new rules, a new regime.
"No matter how long you've been here, whether it's the likes of Giggsy (Ryan Giggs) or myself, we're going to be in the same boat as people like Danny Welbeck, Phil Jones, Tom Cleverley.
"We have got to make sure he feels we're the right people to start each game."
Ferguson's tenure as United boss will end with the club having won the Premier League title for the 13th time under the 71-year-old Scot.
Ferdinand revealed that Ferguson's announcement of his retirement left the United dressing room in hushed silence, but accepts it is the fitting time for his departure.
"He broke the news to us and the thing I remember most is that it was dead quiet in the room, a mad silence," added Ferdinand.
"It was just a combination of disappointment and respect for the manager's decision, and for what he's done for us as individuals and as a team.
"(Winning the title) is the way the manager would have liked to leave the club in his dreams, not looking up at other teams but saying 'come and catch us'."