City's players have been left licking their lips after United threw away a 4-2 lead to draw 4-4 with Everton on Sunday to reopen the title race ahead of next week's derby showdown at the Etihad Stadium.
Mansour told Abu Dhabi TV: "The difference is three points and we do have a chance. But whatever happens and even if we don't win I am very happy and satisfied with the players, the team and the management. They have performed very well and have improved in their last few matches."
The derby is now poised to be the biggest ever as City will go above United on goal difference if they can win on home turf. That means City are guaranteed a first title since 1968 if they can win their remaining three league matches.
Mansour's comments indicate manager Roberto Mancini's job is safe regardless of the outcome of the title race. But while he seems satisfied, those in his employment are determined not to waste a second bite of the cherry.
Midfielder Yaya Toure has told his team-mates they must take advantage of United's slip.
"United's result was amazing," he said. "It was an unbelievable day for us with United dropping points at home. For me, it was strange. We found out about it on the bus on the way to Wolves. It was quite unbelievable and we now have to try and take advantage.
"We did the first part by beating Wolves but we have to settle down and continue to work hard because United still have three points more than us.
"We have to play them at home and, if you look at the record of United, they are very strong away and it will be a very difficult test for us."
United have already won at the Etihad Stadium this season, emerging 3-2 victors in the FA Cup clash between the two in January, although City played the majority of the game with 10 men after the controversial early dismissal of Vincent Kompany.
Source: PA
Source: PA