The 25-year-old joined the now Premier League champions for £24 million in 2011, in the same summer that Cesc Fabregas left for Barcelona, and Nasri says that Wenger had no say in the matter.
"Wenger told me that, if Cesc [Fabregas] left, I would stay but Kroenke wanted the money," Nasri told beIN Sport.
"The coach told me we'll only take Gervinho, Cesc was already gone, I had only one year left so I decided to leave."
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"I am aware that I do not realise a good season," Nasri added. "There are many reasons. But when Mancini said that I'm training at 50% this is not true.
"I felt comfortable against Newcastle. It's been a while since I felt good.
"I do not have regrets. I do not regret joining Manchester City. I want to play and perform. My departure from Arsenal was purely for sporting reasons."
Nasri says that while he has does not regret leaving Arsenal, Wenger is the best manager he has played under, adding that he would not be the player he is without the 63-year-old.
"Arsene Wenger is the greatest coach I have worked with. I only regret not having more discussions with Arsene Wenger when I left [for Manchester City]," Nasri added.
"He's the one who understood me the most and made me the player I am. I'm thankful."