Mancini has refused to concede defeat despite the champions falling 12 points behind United a month ago and being given no opportunity by their rivals to reduce the deficit since.
The Italian is relying on favours from elsewhere but is determined to pounce on any United slip-ups in the two rounds of fixtures before the sides meet at Old Trafford on April 8.
Mancini said: "The next two or three games will be crucial.
"If they lose a point in the next two games - maybe.
"After the two games, we have the derby. But it all depends on us. When you are behind you should win every game.
"We hope we can play a derby with nine, seven points, maybe 10. Less than 12 would be better.
"From the derby to the end of the season, they have three or four difficult games."
City will get the chance to apply some pressure to United as they are the first in action this weekend. City take on Everton at Goodison Park at Saturday lunchtime before United face struggling Reading at Old Trafford in the evening.
But Mancini accepts keeping City's end of the bargain will be tough enough with his side having a poor recent record against the Toffees.
City have lost five of their last seven against the Merseysiders and they played out a 1-1 draw at the Etihad Stadium in December.
Mancini said: "Every game against Everton is very hard.
"It is difficult because Everton are a top team, they play always 100 per cent.
"They are strong, they have good players and a good manager.
"They always play well against top clubs.
"If you want to beat Everton, you should be ready to fight in every position.
"They work hard as a team. For every team it is difficult against them.
"Tomorrow for us will be important."
City will again be without injured captain Vincent Kompany and striker Sergio Aguero.
Kompany has missed seven games with calf problems while Aguero has been back to Argentina to receive treatment on the knee injury that has sidelined him for the last two matches.
Mancini has said on several occasions that Kompany, the Belgium defender, is close to fitness only for his return to keep getting pushed back.
He will now not feature for City at least until they face Newcastle, after the next international break, on March 30.
Mancini continues to play down the seriousness but he accepts the influential 26-year-old's absence is a "big problem".
He said: "Sergio comes back Sunday and Monday, he starts to run here. He needs to do swimming pool strength.
"I think he will be ready for Newcastle.
"Vinny is not in our plans for tomorrow. Also for Vinny, he will be ready, like Sergio, for Newcastle.
"It is difficult because Vinny is a very important player for us but now it is 45 days he is out. This is a big problem."
With Aguero missing, Carlos Tevez, scorer of six goals in his last four games including a hat-trick against Barnsley last week, could again lead the attack.
That would be just days after the Argentinian was charged by police with driving whilst disqualified and driving without insurance.
The 29-year-old could face a prison sentence if found guilty but Mancini has no issues with selecting him this weekend.
Speaking at a press conference, Mancini joked: "The police didn't stop Tevez yesterday.
"This is the problem for tomorrow - because if they stop Tevez, tomorrow Tevez can score three goals!"
On a more serious note, he added: "If he did a mistake, I think it is correct because everyone should respect the rules, but I don't think it is a big problem (for selection)."
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