The US Olympic Committee says it has warned organisers of protests in London and Rio about “further escalation of the situation” in the lead-up to the Games, which start on June 4.
USOC spokeswoman Susan Lattanzio told the BBC that the US was “looking at” the possibility of a protest if a ban on US athletes from Brazil was not lifted.
“If we see further escalation of that situation, we’re looking at it,” she said.
Rio’s Olympic committee has rejected calls for protesters to be expelled from the venues.
“It’s a very serious situation, and we are ready for it to end,” the IOC said in a statement.
Brazil’s President Dilma Rousseff has said she will not allow American athletes to compete in Rio because the country is “being run” by “dictators”.
The IOC says it will not issue a ban until the US Olympic Association agrees to a review of its bidding process.
“The IOC is taking all steps to ensure that the Olympics can go ahead as planned in full,” Ms Lattazio said.
The US has been the most prominent protestor in the US presidential election and has been accused of undermining the US bid with its anti-globalisation rhetoric and its exclusion of minority groups from the bid.
A recent poll by the Associated Press found that only 22 per cent of Americans approve of the job President Donald Trump is doing as president.