United are currently touring the Far East, the fourth time they have done so during Ferdinand's 12 seasons at the club.
But this is the first time the 34-year-old has headed into a new campaign at the club under a boss other than Sir Alex Ferguson, who retired at the end of last season to be replaced by Moyes
However, Ferdinand has already detected a fresh impetus to the Red Devils squad as a result of Moyes' presence.
"It's natural that everybody is trying to impress on this tour," Ferdinand told the club's official website.
"When you get a new manager, you want to show him that you should be in the starting XI for that first day of the new season. That process has started already."
"We've been back from our holidays for more than a week and it's been a really good start.
"It's been very hard but it's been enjoyable and we'll see the benefits of the work we've been putting in back in Manchester and the work we're about to do on tour in the shape of better fitness and a better understanding of the personalities of the players and coaching staff.
"It's a new era for all of us. Hopefully things will come together and we can get off to a good start once the season begins."
United start their domestic season with the Community Shield against Wigan at Wembley on 11 August, with their first Premier League fixture at Swansea six days later.