City underlined their Barclays Premier League title credentials in emphatic fashion last time the sides met, thrashing their rivals 6-1 at Old Trafford in October.
That sensational win served warning of a potential shift in the balance of power in both the city and English football in general.
Now, as league leaders, City could make another strong statement by launching their FA Cup defence with another win over their neighbours and closest challengers - this time at the Etihad Stadium.
But Hart said: "I am not bothered about statements - I am bothered about winning the game on Sunday.
"We want to win every game, regardless of what cup it is in.
"If you do win every game you win trophies, and that is what we want."
Hart accepts United will want revenge for the humiliation they suffered at City's hands last autumn.
"Of course they do but that is for them to feel," the 24-year-old England number one said. "We have got to focus on our game.
"But it has gone, and it has gone for them as well because they have produced some great form since.
"It is nice for the fans to have those memories and those bragging rights but as far as the players are concerned that has gone.
"Sunday is another big game."
The two clubs have been the stand-out performers of the first half of the Premier League season but the form of both has been indifferent of late.
City saw the five-point lead they held at the top of the Premier League wiped out during the course of December as United pulled level.
Doubts were raised over their durability as they were held to a goalless draw at West Brom and then lost at Sunderland over Christmas, but United squandered the chance to take advantage.
United head across town on Sunday having lost successive games to Blackburn and Newcastle, and they now trail by three points again after City recovered from their blip to beat Liverpool in midweek.
Nevertheless, Sunday's third-round tie has been anticipated eagerly in all quarters since the draw was made a month ago.
Hart said: "It is a massive game for the city of Manchester and English football.
"We are the two at the top at the moment and there are going to be some eyes on it.
"They are a privilege to play in, these sort of games.
"I am looking forward to it, hopefully being part of another great encounter."
City have a tough month ahead with a two-legged Carling Cup semi-final against Liverpool and a league clash against in-form Tottenham to come.
They are also set to lose Yaya and Kolo Toure to the African Nations Cup while Mario Balotelli and Gareth Barry are ruled out through injury and suspension respectively.
With doubts over Edin Dzeko and Samir Nasri, City are unusually stretched but Hart remains convinced the club, who are also in the Europa League, can continue challenging on all fronts.
He said: "We have got a good enough and big enough squad to chase everything.
"We feel we can do something this year but to do it you have got to play well and you have got to keep playing well in the big games and hopefully we can do that."
City beat United in last season's semi-finals en route to winning the trophy - their first silverware in 35 years.
It was a success that transformed the mood at and impressions of the club and could well prove a key landmark in the rebirth of City.
Hart said: "It was huge for the club, the fans, the players.
"It helped us bring in some excellent players this year, having that trophy.
"That is what we are all about now - whatever trophy we are in, we are hunting for it.
"It means an awful lot to have that trophy. A lot was made of it.
"There were a lot of local taunts - '35 years'. They have gone now."