The Government wants Birmingham to have a directly elected mayor - and is willing to offer cash and control over transport, housing and economic development if it goes ahead with one.
Chancellor George Osborne has called for a revolution in the way major cities such as Birmingham, Leeds and Manchester are governed, with a high-profile mayor replacing the existing city council leaders.
And Mr Osborne said that "a strong, recognisable city leader" similar to London Mayor Boris Johnson would let major cities "fight your corner in the world".
But the Chancellor also said he would like to see councils working together in combined authorities - raising the prospect of a mayor to represent the West Midlands "city region", including Solihull and the Black Country as well as Birmingham.
Treasury officials said the Chancellor wanted to start a conversation with residents and local leaders such as councillors and MPs about the changes they would support.
Birmingham has considered whether to introduce a mayor as recently as 2012, when it was one of 11 cities to hold referendums.
But residents in the city voted against the change, with 120,611 voters opposed to a mayor and 88,085 in favour.
However, ministers hope residents may change their minds after seeing the success of Liverpool's new mayor, elected in 2012, as well as Boris Johnson.
Speaking in Manchester, Mr Osborne said: "There are big advantages in having an elected mayor to represent your city.
"To have someone democratically accountable to the whole city who can deal with issues like transport or economic development or fighting crime."
He added: "So I am putting on the table and starting the conversation about serious devolution of powers and budgets for any city that wants to move to a new model of city government - and have an elected Mayor."
He also set out plans for a new phase of the planned high speed rail line known as HS2, to connect Manchester and Leeds.
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