"If we hear from the state government that it's not going to be ready, we'll have to move," said Mario Andrada, director for communications at the local organising committee.
Just over one year before the Games begin work on revamping the Julio Delamare aquatic park, alongside the Maracana soccer stadium, has not begun.
A project update in January showed renovations were not yet underway and two sources familiar with the project say no progress has been made since then.
The delays, Andrada said, are because the state government, which owns the property, and the private company that manages it have not agreed the terms of the revamp and future use of the facility.
A decision on whether to change venues would be made "in the next few weeks," Andrada added.
Organisers say they could easily switch water polo from the Maracana, in northern Rio, to the main swimming venue being built at the Olympic Park, to the southwest.
Another possible venue is the Maria Lenk centre, also in the Olympic Park, which was built for the Pan American Games in 2007 and is already the planned site for the diving event.
Possible venue changes have added to the growing concerns about Rio's readiness to host the Olympics, which start in August 2016.
A recent Reuters report showed Rio's preparations were well behind those for London at a comparable stage before the 2012 Games.
Neither the Rio de Janeiro state government or Fina, the international governing body for swimming, diving and water polo, have been available to comment.
(Reporting by Stephen Eisenhammer; Editing by Douglas Beattie)
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