The former Atletico Madrid star confirmed he had split from his wife last month, with Aguero’s son living with his mother in the forward’s native Argentina.
The 24-year-old has endured his first dip in form since moving to City from Madrid in 2011, managing a modest ten goals in 24 appearances for the Eastlands outfit this term.
Despite the turmoil in the striker’s personal life, his compatriot and team-mate Zabaleta is confident Aguero will stay at the Citizens.
“I hope he’ll stay here a long time,” said Zabaleta. “He’s a young player but he’s signed a long-term contract and we want to keep him. He’s an important player here.
“When I speak to him he always tells me he’s enjoying life in Manchester at this club. He’s here to win trophies and to help make this club bigger. I think he’s going in the right direction.
“And we all know how important he is for this club – he was brilliant last season.
“I see him every day. His family were here for Christmas, he had a really good time with them. The private life is always important. If you have problems off the pitch, it’s not easy. Everyone can have problems.
“He’s working really hard for the team and he scored probably the most important goal for this club in the last 50 years. Every fan will have Sergio in his heart.”