The Gunners' challenge has suffered major setbacks in their last two matches. They were thrashed 6-0 at Chelsea on Saturday and were 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 when asked at his pre-match press conference on Friday about Wenger's men, Pellegrini said: "I think Arsenal have a chance of winning the title.
"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."
In contrast to Arsenal, City head into Saturday's 5.30pm encounter in formidable form.
On the same days as the Gunners' meetings with Chelsea and Swansea, Pellegrini's team beat Fulham 5-0 at home and then won 3-0 at Manchester United.
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The Chilean manager 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 stressed 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.
"It is always important for this club, the players and the fans to win the derby against United and we did it.
"Now 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."
Reports had suggested City playmaker David Silva was a doubt for the contest after suffering an injury in the victory against United, but Pellegrini said on Friday that the Spain international will be in the squad.
City's top scorer Sergio Aguero, meanwhile, will miss out for a fourth game due to the hamstring problem he sustained against Barcelona on March 12, with Pellegrini indicating the Argentina striker could make his comeback in the home match against Southampton on April 5.
Pellegrini said: "The team will be exactly the same as last time, with Aguero and Matija Nastasic (who has been sidelined by a knee injury) out.
"Silva is okay and is in the squad list.
"Aguero needs one more week. We will see next week how he improves in his recovery from his injury. He will stay here and work."
Pellegrini refused to be drawn on talk that City are planning to make a move for Arsenal full-back Bacary Sagna this summer.
Asked about that, Pellegrini said: "I have heard so many names through the whole year that I cannot continue talking about all the rumours every week."