The defensive midfielder could be a welcome addition to the squad given the loss of Yaya Toure in January to the Africa Cup of Nations.
Cirigliano is said to be very similar to Javier Mascherano, who had a spell in the Premier League with Liverpool before joining Barcelona in 2010.
According to reports, It is understood that Cirigliano will be in Manchester in the next few days to get transfer negotiations underway.
Cirigliano has previously been linked to Paris Saint-Germain and Manchester United.
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Manchester City have given their backing to trial controversial measures that incorporate safe standing at the Etihad Stadium.
The Football Supporters' Federation (FSF) has become increasingly vocal in wanting to bring back elements of terracing with the Premier League champions, West Ham and Aston Villa all behind the move.
A club spokesman said: "Manchester City Football Club is supportive of initiatives to enhance - safely - our fans' match-day experience, if supported by the appropriate football authorities."
The FSF's Safe Standing Campaign is supported by clubs of all divisions including Brentford, Bristol City, Burnley, Cardiff City, Crystal Palace, Derby County, Doncaster Rovers, Hull City, Peterborough United, Watford, AFC Wimbledon, the Scottish Premier League, the Safe Standing Roadshow and Stand Up Sit Down.
They are calling for the introduction of a pilot of 'railed seats' - new standing technology which are used in Germany. They are metal seats that can be folded up to create wider clearways.
Aston Villa and Peterborough United have already given the nod to a small scale trial of the technology.
Manchester City Fixtures
Saturday December 22 15:00 Manchester City v Reading
Wednesday December 26 15:00 Sunderland v Manchester City
Saturday December 29 15:00 Norwich City v Manchester City
Tuesday January 1 2013 15:00 Manchester City v Stoke City
Sunday January 13 2013 16:00 Arsenal v Manchester City
Saturday January 19 2013 15:00 Manchester City v Fulham
Tuesday January 29 2013 19:45 QPR v Manchester City