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.
However, the call for terracing was recently lambasted by the Hillsborough Family Support Group set up after the death of 96 people at Sheffield Wednesday's Hillsborough Stadium in April 1989.
Chairwoman Margaret Aspinall said: "There are 96 reasons why it should not be allowed. Standing should never, ever come back. I do not think there is anything safe about standing.
"I feel insulted that while people are trying to fight for justice for Hillsborough, that this campaign is growing now."