The transport link, which was a key bid promise when Rio was chosen to host South America's first Olympics, is vital to transport fans from the tourist hotspots of Copacabana and Ipanema to venues where sports such as swimming, basketball and tennis will be held.
"There is a risk of the work not being finished, but there is still enough time to turn it around," a senior city government source said.
At issue is a 1.4 billion reais (£250 million) loan from the BNDES development bank that needs to be released by Brazil's cash-strapped federal government. The money was supposed to be disbursed last year but still has not arrived, a source from the state government said.
On Saturday, Brazilian daily O Globo reported it had seen an email sent by Rio Mayor Eduardo Paes to the local Olympic organizing committee saying there was "a high level of risk" the subway line will fail to meet its deadline.
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The state government denies there is a delay and in a statement sent hours after the newspaper report, said the project was 90 percent complete and only 200 meters (650 feet) of tunnel remained to be dug.
"We are rigorously within the time frame," it said.
Despite such assurances, the city government source told Reuters a plan B has been devised that would use buses with their own express lane to travel the route.
Transport has long been a concern in Rio, where snarled traffic can make travel around the city difficult. Along with the metro line, Rio is building bus express lanes and a light railway to improve transport before the Games.
(writing by Stephen Eisenhammer; Editing by Steve Orlofsky)
