The United States is in the process of discussing with the Greek government whether the armed soldiers, whose home base in Germany, would be sent to Athens, the site of the games, to nearby island Crete where the U.S. team will train, or remain on alert in Europe, the official said.
The decision on where to position the soldiers is mostly up to the Greek government but will be made jointly with Gen. James Jones, the top NATO commander who also is commander of U.S. forces in Europe, said the official, on condition of anonymity.
In any event, there will be up to 50 communications and other liaison personnel assigned to the Games, the official said.
Shadowing the Aug. 13-29 Games in the country in which they originated is fear of terror attacks. The United States plans to send State Department Diplomatic Security agents as well as FBI agents to Greece.
Israel, which lost 11 athletes to Palestinian terrorists in the 1972 Games at Munich, Germany, will send armed guards and is among a half-dozen countries contributing security expertise at Greece's request.
Still, the brunt of securing the Games rests on the shoulders of the Greeks, whose pride at being the hosts is tempered by private concerns. Greek officials have said confidently that they are on top of the security problem.
Greek police and U.S. counterterrorism sources told The Associated Press earlier this month that armed U.S. agents would watch over athletes during a pre-Olympic training camp on the island of Crete.
Also, a Greek official said Wednesday in Athens that the Games' security budget, already the highest in Olympic history, was now about $1.5 billion.
In May, the United States provided Greek police and border officials with radiation detection equipment to help guard the Olympics against a nuclear or "dirty" bomb.
Greece has held a number of exercises to deal with mass casualties from a nuclear, biological or chemical attack. NATO, which has been asked by Greece to provide aerial surveillance during the games, also has promised to fly in medicine and rescue equipment if such an attack occurs.
CBS News consultant Ret. Army Col. Mitch Mitchell, a terrorism expert, went to Athens as part of a team to help the government of Greece evaluate its security measures against terrorism, the strength of its anti-terror and counterterrorism programs and their resources for consequence management.
He says Athens should be safe for the Olympic games but there are still some things to consider.
"Greece is a crossroads of Mideast traffic and so a lot of people go through that country and they might drop off a few to stay and cause trouble during the Olympics," Mitchell said. "That's what we're trying to prevent."