Despite the club's obvious advantage in terms of available funds, the Italian says that the Gunners captain will face a difficult choice over where to go should he leave north London, and he is in the dark as to how the saga will end.
"I don't know what will happen with Van Persie," Mancini told the Daily Mirror. "Now he's an Arsenal player.
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"When you are talking about Manchester City, United and Juventus it's difficult for any player to choose between these three teams.
"But if we have a chance to take him, we will try. He is a top striker like the other strikers we have."
The Italian manager also claimed that his current squad is not good enough to win the Champions League, and that their main priority will be to try and retain their Premier League title, this season.
"Defending the title should be our target this year," Mancini added.
"If we also go well in the Champions League, there could also be a chance that we can arrive in the quarter, semi-final or final.
"We will try to win it but it's important, for this, that we have a good squad.
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"But the Champions League is a strange competition sometimes. I don't say Chelsea didn't deserve to win it, but there were better teams than them last year.
"Chelsea probably deserved to win a Champions League three or four years ago, but there are some years when you can [win] a Champions League and not know why.
"Our target for the Champions League should be to go for the second stage after the group."