The cash-strapped MTA has quietly reopened the bidding for its Madison Avenue headquarters site in hopes of raising more money from the sale.

The agency is seeking fresh proposals from real-estate developers, citing changes to the Midtown East rezoning proposal, after receiving a first round of bids in mid-August.

Developers now have until 5 p.m. Oct. 16 to amend their bids or submit new proposals.

The MTA plans to award a long-term lease to a developer who will be able to demolish its headquarters along with two adjoining buildings and redevelop the location.

The agency, which announced in April 2011 that it would sell the properties and vacate the site, posted a notice on Sept. 25 seeking new bids.

As an enticement, the winner “will be able to commence the Redevelopment under the proposed upzoning immediately after the MTA vacates the Property,” according to the notice.

The previous zoning plan would have pushed off redevelopment until 2017 to kick start the Hudson Yards project. The zoning still has to be approved by the City Council and signed by the mayor, who has made this a centerpiece of his last year in office.

Not only can development start two to three years sooner, but the MTA is likely to get a higher price for the long-term lease of its now more valuable property that takes up the entire east side blockfront from E. 44th to 45th streets.

“The MTA will benefit from this provision,” said Steven Spinola, president of the Real Estate Board of New York.

Cushman & Wakefield, the MTA’s brokerage firm, declined comment.