City boss Roberto Mancini believes the former Manchester United midfielder needs up to six weeks with fitness work before being ready, according to the Daily Mail.
Hargreaves said: “It’s important that you get back into a rhythm of playing football and I haven’t done that for a while. There’s tons of games to come this season in various competitions.
“I’ve never not played in the Champions League, it’s pretty much been standard for me every season.
“I like to measure myself against the best and I’ve always taken on challenges – I left Canada for Germany as a kid, I’ve left comfortable situations.
“It’s a fantastic group of players here, and I hope that I’ll be a good addition to these guys to help out.”
Hargreaves joined City on a one-year deal on Wednesday. The midfielder was available on a free transfer after having been released by Manchester United after struggling with injuries during his spell at Old Trafford.
City full back Wayne Bridge has also been left out of the Champions League squad.