Although Leeds go into the new decade as clear leaders of League One, the Elland Road club began the century as title challengers, ending the 1999-2000 campaign in third place behind champions United and runners-up Arsenal.
Severe financial problems sparked the Leeds slide, but Ferguson expects the club to reclaim their top-flight status after being revitalised by Grayson.
Ferguson said: "I watched Leeds against Liverpool in the League Cup earlier this season and I thought they did really well. Simon Grayson has done a fantastic job there.
"He is a Leeds boy himself and a former Leeds player. Some people have targets in life and I think he has reached his managing Leeds.
"He has instilled great motivation in his team. They have not let him down and I don't think they will be too far away from the Premier League in the next couple of years.
"They look to be an absolute certainty to be in the Championship next year and the motivation that is coming from the manager means they have a great chance of being in the Premier League in the next couple of years.
"The first problem with Leeds was financial because they had to sell their best players. They had quite a few good players Mark Viduka, Harry Kewell, Alan Smith all these players were sold on and that's what happens if you are financially strained. If you sell your best players, you can bet your life that the results will change too."
Clashes between the two clubs have often been spiky affairs, with enmity between the supporters off the pitch being matched by the passion displayed on it.
And with 9,000 Leeds supporters due to make the trip from West Yorkshire, Ferguson insists the players must be aware of their responsibilities.
He said: "It will be a fantastic feisty occasion. Every time we have met, it always carried a degree of hostility.
"That has meant we had to tell the players to behave themselves on the pitch because there was no need to add to the problems off the pitch.
"Leeds are bringing 9,000 fans and it is going to be a busy day for the police, it will be a brilliant atmosphere.
"I used to enjoy the games and we had some great games over there. The atmosphere was always electric at Leeds."
United have won the FA Cup just once in 2004 since withdrawing from the competition in 2000 and Ferguson admits he is hopeful of a change of luck this season. "We have targets in the league and the European Cup, but you would not discount an FA Cup would you?
"Last season we were knocked out of the semi-final on penalty kicks and, in 2007, we lost the final in the last couple of minutes to Chelsea.
"Before that, we lost to Arsenal in the final on penalties. We were unlucky then and you need luck in the Cup. It should be called the Luck Cup because every time we have won it, we have had bits of luck on the way."