Aguero confirmed earlier this month that he had split from his wife and admitted that it was difficult with his son being back in his native Argentina.
However, while Zabaleta acknowledged the importance of a player's private life, the full-back expressed his belief that Aguero will not be leaving the Premier League champions.
"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."
Aguero played a key role in City winning the title last season following his arrival from Atletico Madrid and Zabaleta says the club are now big in Argentina, with Carlos Tevez also in the squad.
He added: "After we won the title, people were talking about Sergio's goal and that game for a week.
"Now in Argentina people love to watch every City game. You will soon see more Argentinian players in this league.
"People talk a lot about City over there. Real Madrid and Barcelona are probably talked about more, but City are a massive club now in Argentina.
"You see shirts with Aguero or Tevez on. More than Man United? Yes - in my home town anyway."