The club have opened an exhibition at the stadium, which currently holds around 47,500, to seek further the views of fans, residents and other stakeholders in the latest stage of an already comprehensive consultation process.
City intend to make a formal application for planning permission in December and, if it goes ahead, the work would make the stadium the third largest in the Premier League.
The plans are the latest evidence of the rapid growth of City on and off the field under their Abu Dhabi owners. They already have one large construction project under way with their new £200million academy and training complex due to open in a year's time.
Two options for stadium redevelopment are being considered, with the most likely being that work to the South Stand is first undertaken to initially take capacity to 54,000. Following completion the North Stand would then be extended.
The second option is to press ahead with expansion on both sides of the ground concurrently.
City state that the work would allow them to introduce a new season card priced at £299 and improve hospitality offerings.
City's head of infrastructure and corporate responsibility, Pete Bradshaw, said: "Manchester City Football Club strives to provide its supporters and visiting fans with one of the best possible matchday experiences in the Premier League and European football.
"Games are selling out frequently prior to going on open sale and there is rising demand from supporters for more season tickets, matchday tickets and premium seating.
"This is why we are considering these expansion proposals.
"We will be in touch with every fan who would be potentially affected by the changes in phase one, and we encourage fans, residents and anyone who has a point of view, to visit the exhibition in person or online and tell us what they think."
Visitors attending the free exhibition will have the chance to give their thoughts in a questionnaire.
This opportunity will run throughout July and August and will be followed by a formal consultation process in the autumn.
Planning permission will then be sought from Manchester City Council at the end of the year.
The council are the owners of the stadium having built it for the 2002 Commonwealth Games but City have a 250-year lease to play there.