City suffered a disappointing draw with Stoke last weekend and then crashed to a dramatic 3-2 defeat against Spanish champions Real Madrid in the Champions League on Tuesday.
They go into Sunday's game hoping to get back to winning ways, but Mancini is expecting a tough test against a team who has been in good form of late despite losing Robin van Persie and Alex Song last month.
"I don't think we have an easy game," Mancini said. "When you start the season after a European Championship, you have problems with some injuries. I don't think it will be easy. It is important that we do a good performance.
"I think Arsenal can compete for the title. I don't know if they are better than last year but there is less pressure than last year.
"They have lost two or three important players but I am sure they will play for the title.
"Arsenal have good players, Manchester City the same. It is a good game for people who come."
One of City's ex-Gunners, Samir Nasri, will miss the game with a hamstring injury suffered in Madrid, but Argentina striker Sergio Aguero could feature despite not making an appearance from the bench in Spain after recovering from a knee injury.
Mario Balotelli is also set to be included in the squad following his omission in midweek and reports of a bust-up between the Italian striker and Mancini.
"I don't think Samir will be ready for Sunday, I hope for the next game," Mancini said.
"Sergio is fit. We are unlucky because I wanted to put him on at the Bernabeu but we had two injuries."
Arsenal's campaign has taken a significant upturn after successive goalless draws in the opening two games of the season prompted early mutterings about the club's prospects.
Last weekend's impressive 6-1 home defeat of Southampton has diminished fears that Arsene Wenger's side will not be able to compensate for the loss of van Persie's goals and, while the midweek Champions League victory in Montpellier was no stroll, it nonetheless provided the Gunners with their third successive victory.
Winning at Eastlands will prove far harder, but three points on Sunday would intensify the optimism that is slowly growing at Arsenal and Wenger believes this game will provide a clear indication of his side's title credentials.
"It will tell us a lot about our quality. How we handle the big games will decide how well we do in the championship," Wenger said. "That is why it is an interesting weekend for us.
"I have no doubt about the desire and hunger of my squad. It will just tell you how strong we are at the moment.
"I believe we are quite strong but we have some room for improvement. All is not perfect but the signs we are giving are very good and very strong.
"The hunger is massive in this squad. They want to do well. They are focused. They want to win.
"We want to continue to improve because we have many new players. It is a big test to see how strong we are."
Arsenal were handed some good news this week when England midfielder Jack Wilshere returned to full training for the first time in over a year but, like Emmanuel Frimpong, he is still some weeks short of a first team return.
Bacary Sagna and Tomas Rosicky are also missing and are not expected to return for at least three weeks.
Source: AFP
Source: AFP