The newspaper said sources it identified as close to the matter say Dolphins executives and Miami-Dade County Mayor Carlos Gimenez expect to announce the referendum agreement Monday.
Under the new scenario, Sen. Oscar Braynon, D-Miami Gardens, would change his proposed legislation to require a countywide vote on the plan, a source said.
Dolphins executives want the vote by May 22, which is when the NFL is expected to name the 2016 Super Bowl site. The Dolphins are bidding to host the big event.
Club owner Stephen Ross has agreed to use private dollars to pay for at least $201 million of the project, with state and county taxpayers picking up no more than $199 million.
As recently as last month, Ross was opposed to voters having a say, contending there wasn't enough time, The Herald said. But the stadium bill didn't make area lawmakers' priority list for this year's session, prompting the Dolphins to rethink their position, the newspaper said.