Samples taken at the World Cup will need to be flown across the Atlantic to Switzerland, raising doubts that positive tests from players will be discovered before their next matches.
"The rather disappointing situation is the new laboratory which is to be ready for the Olympic Games in 2016 I'm afraid will not be ready for the World Cup," said Reedie who is also an International Olympic Committee vice-president.
"That makes the job of (soccer's ruling body) FIFA that little bit more complicated and I understand they're going to take the samples to the Lausanne laboratory which is one of the really good ones," he told Reuters in an interview.
WADA said in August the Rio de Janeiro laboratory did not meet the International Standard for Laboratories (ISL).
Reedie, who took over the WADA presidency at the start of the year, quashed doubts that samples would not be tested in time in Brazil.
"FIFA can do it because in football there's about a four or five-day gap between matches so the turnover of samples in Lausanne can be done quickly enough so that the process...will actually work," he added.
(Editing by Tony Jimenez)
