Leaders for so long, City will take the field in north London eight points behind if Manchester United beat QPR earlier in the day.
Mancini acknowledged earlier this week that defeat to the Gunners in such circumstances would end his side's challenge for good, but the Italian was in no mood to surrender ahead of the weekend.
He said: "I don't believe this championship is finished. If United win all their games, congratulations. They deserve to win the title.
"But seven games from the end I think anything can happen. We lost four points in two games. It is possible to happen to them."
And Mancini has told his players Sunday's game is the time to prove they have the bottle to make a fight of it.
"In this moment it is important to be strong," he said. "It is easy to be together when you are on the top for seven months and you win every game."
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