Frenchman also says that when they visit London on Sunday, Roberto Mancini's men aim to play the kind of football that saw Liverpool secure a 2-0 win at Stamford Bridge recently
The Red Devils are currently two points behind the league leaders, but have played one game more, while Andre Villas-Boas' men are 10 points behind, in fifth place in the standings.
City travels to London to play Chelsea on Monday night, with the Blues having just qualified for the knockout round of the Champions League as group winners, in contrast to both Manchester clubs, who bowed out of the competition.
Nasri believes that City's arch-rivals pose more of a threat on the domestic circuit.
"Man United are still the threat to us," said the Frenchman, according to The Sunday Mirror. "I say that because they have more experience than any other team. It will be difficult when we play Chelsea, of course, but we knew it would also be difficult going to places like Spurs, Man United and Liverpool - and we had great results against those teams.
"So I don’t know what we have to fear about Chelsea."
Concerning the game plan against the Blues, the 24-year-old midfielder conceded that City will look to play a similar style of football that Liverpool employed when it emerged victorious at Stamford Bridge.
"We are confident about our quality and we will try to play the same game that Liverpool did when they beat Chelsea in the league at Stamford Bridge," Nasri said. "We know that if we press them high and play our football, then they will be in difficulty."
But in the long run, Nasri admitted that City is looking to emulate Barcelona, who has won the Champions League twice, La Liga thee times and the Copa del Rey once in the last three seasons.
"Our model is Barcelona," he said. "As a team we defend very high up the pitch and I believe that’s why we are scoring so many goals. When you win the ball in the other team’s half it will always be easier to score because you are closer to goal. You have less distance to run and you are fresher running just 30 metres.
"We cannot win the Champions League now, but our objective at the start of the season was the [Premier] League."
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