The 24-year-old forward has split from Giannina, who is the daughter of Argentina legend Diego Maradona, and she and their baby son Ben are now living in Madrid.
However, compatriot Zabaleta thinks the striker, who has scored eight goals this season, is enjoying life in Manchester and will stay in order to win top trophies and maintain a strong bond with the club's supporters.
“Sergio is still happy in Manchester. His family came here for Christmas and New Year and he spent some really good time with them," he told reporters.
“Having a happy private life is always important and when problems arise it is never easy because we are only human. But Sergio knows how important he is to City and he is always telling me how he is enjoying life in Manchester."
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He continued: "When clubs sign top players they want 100 per cent commitment and Sergio came here because he wants to win all the important trophies.
"Last season he scored the club's most important goal for perhaps the last 50 years, so the fans love him."
City travel to Arsenal on Sunday, while Premier League leaders Manchester United host Liverpool, and Zabaleta insists his side cannot afford any more slip-ups considering they are already seven points behind Sir Alex Ferguson's men.
"It's been a long time since we won at Arsenal, but it was a long time since we won the league," he added. "Last season, when we lost there, we were eight points behind United and we thought it was over.
"We are under pressure again because we can’t drop any more points as United have a seven-point lead. If the gap becomes bigger then it will be very difficult for us."