United are odds-on favourites to claim their 20th league crown after opening up a seven-point gap on their rivals, who wrestled the title away from them on a dramatic final day last season.
But Kompany pointed to the eight-point margin City overhauled last term and believes his side are ready for a repeat performance.
The Belgian said: "A couple of years ago, if we had fallen seven points behind, we would have said it would be very difficult.
"But now we have done it and won the title, nobody panics. Everything is still possible.
"We have proved what we can do and everybody is very calm. That's the advantage you get when you win it once.
"You have that inner confidence and although the media and the fans get excited, we don't."
Kompany conceded that it would be a tough task, but claimed City were playing well enough to reel in United.
He added: "We are perfectly capable of having a long winning streak that will bring us very close. We have set our standards high and worked hard for a long time to bring ourselves into this position."
City will have to maintain their title challenge without the services of midfield driving force Yaya Toure as a heads for the Africa Cup of Nations.
But defender Pablo Zabaleta has urged all his team-mates to step up to compensate for the loss of the Ivory Coast star, his brother Kolo and back-up striker Abdul Razak.
The Argentina international said: "It's going to be a very tough time for us because we're going to lose Kolo, Yaya and Abdul, three important players.
"Yaya has been a regular player for a long time. We know how important Yaya is to the team but there are other players who can do the same job.
"Everybody is important for the team and we need to keep working hard.
"Last season, January and February was when we dropped points and we need to try to make sure that doesn't happen again."