The 31-year-old was signed by Roberto Mancini on a one-year deal last August but the England international made just four appearances for the Premier League champions.
Ex-Bayern Munich midfielder Hargreaves made his City debut against Birmingham City in the Carling Cup and scored the opening goal in a 2-0 victory.
Sir Alex Ferguson made the decision to release Hargreaves last summer after the £20.2m signing had struggled to overcome a persistent knee injury which had restricted the midfielder to just 18 Premier League starts since moving from the Bundesliga in 2007.
City manager Mancini said the Eastlands outfit chose to take a gamble on Hargreaves because of his “fantastic” quality, but conceded that the move has not worked out.
“We took a gamble on Owen because he was such a fantastic player,” Mancini told Sky Sports in February.
“We thought we could try to get him fit in two or three months and then he would be able to play. But it hasn’t worked out quite like that.
“When you have a player who hasn’t played for two years and he starts to train every day there are small problems all the time. Problems in the knees or the hamstrings. So Owen hasn’t been able to play when we have needed him.
“He may play again this season but he is not ready now. I hope eventually he will be able to play all the time. He deserves to, because he is a really nice guy.”
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