United handed Arsenal a humiliating 8-2 defeat at Old Trafford in August as the Gunners made their worst start to a season for 58 years.
Wayne Rooney led the rout with a hat-trick and United scored five times in the final 26 minutes to rub salt into Arsenal's wounds.
However, Arsenal have since recovered from that embarrassment to reach the knockout stages of the Champions League, and they start the weekend in fifth spot, four points behind fourth-placed Chelsea.
And United manager Ferguson claims the Gunners will have forgotten about their miserable performance five months ago.
"They've recovered well and qualified for the next stage of the Champions League so there's not a lot wrong," he said at a press conference on Friday.
"You have to forget it. I've never used revenge as part of my motivation. It rankles I'm sure, but you have to forget it and I'm sure Arsene has done that.
"Thinking of revenge has never played a part in my managerial career. It just doesn't apply itself to me."
United start a big weekend three points behind City, who entertain third-placed Tottenham just hours before Ferguson's team kick-off on Sunday.
Defenders Chris Smalling and Phil Jones have recovered from knocks and are available for the start of a crucial run of games for United.
They face Liverpool twice - once in the league and once in the FA Cup - Chelsea and Tottenham in quick succession, and Ferguson added: "It's the start of a hectic spell for us.
"It's a fantastic run of game and a programme we hope we come through very well because it could decide a lot of the season."
Ferguson, who refused to discuss reports that keeper David de Gea plans laser surgery to improve his vision, believes the reurn of iconic striker Thierry Henry to Arsenal is a shrewd move by Wenger.
United have also brought veteran midfielder Paul Scholes out of retirement, and Ferguson said: "There was talk about Henry last January and Arsene decided against it. For me there's no negatives at all.
"It's similar to our situation with Paul Scholes. When I saw they had erected a statue to him (Henry) I thought it's a nice lead to bring him back for short spell.
"You saw how the fans reacted when he scored the goal against Leeds United in the FA Cup. It was fantastic.
"He's still a great player. Most of the players probably didn't play with him when he was last there so they are going to be motivated by him. He's one of the greats of Arsenal's history."