Officials speaking on condition of anonymity said the satellite had lost power and propulsion, and could contain hazardous materials.
The White House said it was monitoring the situation.
A spokesman said "numerous" satellites had come out of orbit and fallen back to Earth harmlessly over the years.
"We are looking at potential options to mitigate any possible damage this satellite may cause," said Gordon Johndroe, who speaks for the US National Security Council.
Questioned by The Associated Press, he would not be drawn on whether the US would try to destroy the satellite, perhaps with a missile.
An unnamed official quoted by AP said the US government was keeping lawmakers and other countries abreast of the situation.
Fuel hazard
The satellite contains the rocket fuel hydrazine, a government official told AP on condition of anonymity.
A colourless liquid with an ammonia-like odour, the fuel is a toxic chemical and can cause harm to anyone who comes in contact with it.
John Pike, director of the defence research group GlobalSecurity.org, said an uncontrolled re-entry could risk exposure of US secrets.
Spy satellites typically are disposed of through a controlled re-entry into the ocean so that no one else can access the spacecraft, he was quoted by AP as saying.
The military expert believes that shooting the satellite down would create debris that would then re-enter the atmosphere and burn up or hit the ground.
In his estimate, the satellite weighs about 20,000 pounds (9,072kg) and is the size of a small bus.
It is possible, he adds, that this one died as long as a year ago and is just now getting ready to re-enter the atmosphere.
Another expert, Jeffrey Richelson of the National Security Archive, said the satellite is probably a photo reconnaissance satellite.
Into the ocean
AP notes that the largest uncontrolled re-entry by a US space agency (Nasa) craft was Skylab.
The 78-tonne abandoned space station fell from orbit in 1979.
Its debris dropped harmlessly into the Indian Ocean and across a remote section of western Australia, the US news agency says.
In 2002, officials believe debris from a 7,000-pound (3,175-kg) science satellite hit the Earth's atmosphere.
It rained down over the Gulf, a few thousand miles from where they first predicted it would crash.
