It would also potentially be the first time a major sporting event turned to the general public, and their extra rooms, to solve a short-term spike in demand for accommodation. By contrast, in London for the 2012 Olympics some home owners faced potential fines for renting their properties during the Games.
Airbnb declined to comment.
Read MoreInside the sharing economy: Airbnb fight heats up in NYC
The two other short-listed firms are AlugueTemporada and Hotel Urbano.
Accommodation in Rio has long been a concern for the International Olympic Committee and it was singled out again as an area where progress needed to be made by Nawal El Moutawakel, IOC Coordination Commission Chairperson, at a news conference in Rio on Wednesday.
Speaking at the same conference, Carlos Nuzman, president of the Local Organising Committee, said Rio already had 36,000 of the 40,000 or so rooms it needs for the Olympics. But he added that the committee was working to secure more accommodation.
"We might be in a position in which we can offer much more than forecast and the additional supply could reach 18,000, half of the total amount we have at the moment," Nuzman said.
Partnering with a company such as Airbnb could also help to provide more economic options for visiting fans. The football World Cup, held in Brazil in 2014, was criticized for the cost of accommodation, particularly in Rio where the final was played.