As it happened, Sao Paulo had just such an arena: Cicero Pompeu de Toledo Stadium, known as "Morumbi," standing amid a sea of orange-roofed mansions on the western side of the city.
But after nearly three years of negotiations and delays, World Cup organizers instead opted to build a brand-new stadium on the poorer eastern edge of town - a decision that involved a popular former president, one of Brazil's most bitter football rivalries, and no small degree of controversy.
Scrutiny of that decision has intensified following a fatal accident on November 27 at the building site of the new stadium, called Arena Corinthians. A crane collapsed while lifting a 420-tonne piece of roof into place, crushing a portion of the facility's exterior and killing two workers on the ground below.
The accident has pushed back the stadium's estimated completion date from December to April, according to FIFA, the governing body of world football. That is perilously close to the June 12 date for the World Cup's opening match, between Brazil and Croatia, which Arena Corinthians is due to host.
Officials are still probing the causes of the crane collapse, and there is no evidence that the company building the stadium, Odebrecht SA, committed any wrongdoing. Odebrecht said in a statement that construction "has followed rigorous planning and respected the appropriate speed."
The stadium's supporters say the 68,000-seat facility will help support economic development in a depressed area of mostly one-story houses some 12 miles (20 km) east of downtown.
"This area has been ignored for years, but this stadium will be a source of pride and much more," Andres Sanchez, a former president of the Corinthians football club, said in an interview earlier this year. Corinthians will own the arena when it is completed.
To some critics, the recent accident is particularly galling because they say the stadium should never have been built in the first place. They say its troubled history is emblematic of the poor planning, murky negotiations and wasteful spending that have become big political issues here as the Cup draws closer.
In Image: An aerial view of the area where a crane collapsed, on the site of the Arena Sao Paulo stadium, known as "Arena Corinthians", which will host the opening soccer match of the 2014 World Cup, in Sao
Text and Images: Reuters