Ferdinand has won six Premier League crowns since joining the Red Devils in 2002, the latest last season in Sir Alex Ferguson's final campaign in charge.
With former Everton man Moyes now in charge, Ferdinand is targeting a 21st title for the Old Trafford outfit.
He told The Sun: "To win the league under David Moyes would be phenomenal.
"Last season was one of the best when we won title No 20 but this could go beyond that.
"To win it at the first attempt with a new man in charge would be something special."
Ferdinand believes Moyes will be able to build on the solid foundation left by Ferguson.
"Moyes is a real football man and an honest guy," the veteran defender added.
"His hard working ethic reflects the man himself and he obviously wants success. We've got a great chance with this manager.
"Every year when we have the end-of-season party we are thinking about the next season and what we are going to do.
"We always talk about improving on the previous season. That was no different this year just because the manager has changed."
Jose Mourinho's return to Chelsea will make it harder for the Red Devils next season and while 34-year-old Ferdinand is pleased to see him back, he hopes he is not successful.
"As a fan it's good to see personalities like Mourinho coming into our league," he added.
"But, hopefully, he can wait till I've retired before he wins anything at all."