The Gunners' challenge has suffered considerably of late, with them being thrashed 6-0 at Chelsea on Saturday and then held to a 2-2 draw at the Emirates Stadium by Swansea on Tuesday.
Ahead of their home clash with City on Saturday, they are fourth in the table with 63 points from 31 games.
Their third-placed visitors are three points better off with 66 and have two games in hand over them - as well as over second-placed Liverpool, who are on 68 points, and leaders Chelsea, on 69.
Arsenal manager Arsene Wenger has stressed he and his players have not given up on the title.
And asked on Friday if he thought City would put Arsenal out of the race if they beat them on Saturday, Pellegrini said: "It will be difficult for them of course.
"It is difficult for them because they have three teams in front of them at the top of the table. But in football, the mathematics give you a chance.
"Maybe they didn't play well or have the results they needed in the last two matches.
"But I think that all the teams will drop points also from now until the end of the season, so I continue thinking that Arsenal have a lot of chances to fight for the title."
On the same days as Arsenal's meetings with Chelsea and Swansea, City trounced Fulham 5-0 at home then won 3-0 at Manchester United, and Pellegrini is keen for his side to keep up their momentum in what he regards as a vital match for their run-in.
But he certainly does not expect victory on Saturday to come easily, and has also emphasised that the fixture is not the be-all and end-all for City's title push.
"It was a very good start to the week, and we hope we finish in the same way," Pellegrini said.
"We must continue by trying to win the next match and continue fighting for the title.
"This is a big game because it is against a team that is fighting for the title also.
"But it is not the last match and not the match that will decide the title. It is a huge step for continuing in the way we are going so far.
"Maybe Arsenal did not have a good week but they continue being a very good team.
"They are playing at home, they have very good players and I am sure that we will need to do a very good game if we want to win."
Pellegrini has refused to go along with talk of the trophy being City's to lose, and when asked on Friday if he thought his players could "smell the title", the Chilean said with a smile: "We are not thinking of smelling anything - we are just trying to win every match.
"Every game, it is the only way. All the smelling, or thinking about favourites - I don't think it's the best way to do things."
Pellegrini stressed the club's owners have not demanded that he adds the Premier League crown to the Capital One Cup he has already guided City to this season, his first in charge.
And the 60-year-old has also expressed his admiration for Wenger's longevity as Arsenal boss.
The Chelsea match was the 1,000th game at the Gunners helm for Wenger, who was appointed in 1996, and while Pellegrini cannot realistically hope to match that stint, he is keen for an extended spell with City.
"It's a good way of working - the best way, I think," Pellegrini said.
"Maybe one of the most difficult things for a manager is to stay so many years at the same club. That's why I have respect for Arsene Wenger.
"It's a bit late for me! 17 years more? I think I will be a little bit old!
"But I'm very happy here and I will try to continue for the most amount of years that I can."
Pellegrini confirmed City playmaker David Silva will be in the matchday squad for Saturday's contest, despite reports having suggested the Spain international was a doubt due to a problem he sustained in the victory over United.
Sergio Aguero, meanwhile, is not yet ready to return to action after the hamstring injury he sustained against Barcelona on March 12, with Pellegrini indicating the Argentina frontman could make his comeback when City host Southampton on April 5.