Former Manchester United midfielder Hargreaves joined City last week in the hope of reviving his career after three injury-ravaged years at Old Trafford. The 30-year-old is not yet match-fit and has been left out of City's Champions League squad but Mancini believes he will go on to play a big role this season.
"He had a big problem in the last two years but he can recover very well and be a very important player for us," said Mancini.
"I think he can play in maybe two or three weeks and he can always play. He is 30 years old, he is young and he was very unlucky. If he can recover very well it will not be a problem."
Another player unlikely to come into contention until later in the month is defender Kolo Toure, who is now available again after serving a six-month ban for failing a drugs test.
"It depends," said Mancini. "He is fit but he needs to play. I think in two weeks he can play."
Mancini again had to answer questions about controversial striker Mario Balotelli's off-field behaviour as he held his regular pre-match press conference on Friday morning. The Italian has rarely been far from the headlines since joining City last year and has had another interesting week while back in his homeland.
The ?24million man was mobbed while visiting a prison in Florence, called as a witness in a mafia trial and accused of using his iPad while on the Italy bench during a match against the Faroe Islands.
Mancini, who clashed with Balotelli during the pre-season tour of the United States, believes everything concerning the player is blown out of proportion.
He said: "I'm disappointed because everything Mario does is a big situation. I think he played well for Italy on Tuesday. This is important. The other situations are not a problem. Mario is 21 years old. He can change in two months, three months, six months."
Source: PA
Source: PA