FIFA are determined to ensure Estadio Beira-Rio will host matches at the World Cup amid concerns over the venue's readiness.
The mayor of Potro Alegre, Jose Fortunati, on Monday expressed his fears that stadium renovations would not be able to be completed in time for the showpiece tournament, which starts in June.
Fortunati warned that the city in southern Brazil may miss out on hosting matches if a bill to allow tax breaks for companies investing in temporary structures for the competition is not voted in.
He told Radio Gaucha: "This is the point which matters in terms of holding the World Cup in Porto Alegre.
"If the bill is not voted, we will not have the World Cup in Porto Alegre. This is because we will not have the resources to do it. We have no plan B. The only alternative is this."
When contacted by Perform on Tuesday, FIFA stated that they will do all they can to ensure work on all of the the 12 stadiums is complete for the eagerly awaited finals, and that the situation should be made clearer later this week.
A FIFA spokesperson said: "As said previously, the FIFA World Cup will be played in 12 venues. FIFA, the Local Organising Committee (LOC), the federal government and the respective host cities are working together this week in Rio de Janeiro to find solutions to the remaining challenges.
"There will be a detailed update on Thursday at approximately 12:30 Brasilia time following the Local Organising Committee meeting at a media briefing in Maracana."
France and Honduras are due to meet in the first game at Estadio Beira-Rio in Group E on June 15, with a further three group matches scheduled for the stadium, as well as a last-16 encounter.