The Blues captain has spent the last month at home in Argentina as he represents the national team in the Copa America.
“It is with great regret that I have to inform Manchester City of my wish to leave the club,” he said in a statement.
“I hope that the people understand the difficult circumstances I have been living under the past 12 months, in regards to my family.
“Living without my children in Manchester has been incredibly challenging for me. Everything I do, I do for my daughters, Katie and Florencia. I need to be closer to them and to spend more time with them.
“I need them to be happy because my life is about them now. I need to be in a place where they can adapt.
He added that he his time at Eastlands has made him “very proud” and assured fans of his dedication to the club on the pitch.
The prospects of a transfer for the 27-year-old, who has three years to go on his current contract, are hampered by the club’s valuating him at £50m and his weekly wage of over £200,000.