The 71-year-old, who retired from football management in the summer, has confidence in his fellow Scot's ability to steer the team to success.
"For David, winning a trophy would be a fantastic achievement, no matter what it is - the League Cup, FA Cup, European Cup or Premier League," Sky Sports News quotes Ferguson as saying. "We've always had priorities obviously and David is aware of that but I hope he achieves it.
"The key for David is not to look to do anything better or less but just to maintain what the club has been for 20-odd years and keep the success going. It is not easy winning a trophy in our league because you could say there are six teams fighting for the league.
"He has great support at the club. It is a fantastically-run football club. There are absolutely no issues about it. Every club needs a little bit of luck and hopefully we'll get the luck."
United are currently eighth in the Premier League table with 11 points from eight matches.