The Greek-U.S. exercise last week evaluated the ability of the security forces to respond to 77 scenarios that also included a rocket attack on a plane, a suicide bombing, the poisoning of the chief Olympic organizer and terrorists holding hostages on the Queen Mary 2, one of eight cruise ships that will be used to accommodate Olympic officials and spectators, the newspaper said.
It is not certain whether Blair will attend the Aug. 13-29 Games and his name could have been used to represent any foreign leader in the drill. Greek police refused to comment on the report.
Some 300 security personnel have been participating in a three-day training program code-named "Olympic Guardian Two." About 70-thousand police officers and soldiers will patrol Athens come August.
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 their security measures against terrorism, the strength of their anti-terror and counterterrorism programs and their resources for consequence management.
He says Athens should be safe for the Olympic games -- Greece has put over $1 billion into security -- 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."
Olympic teams and athletes choosing to stay at hotels or other sites outside the athletes' village must take responsibility for their own security during the Athens Games.
IOC president Jacques Rogge, speaking at the end of an executive board meeting Wednesday, said national Olympic committees are free to bring their own security personnel as at previous games.
"This is not a new procedure, it's been done before," Rogge said, noting the Belgian team had its own security when he was the delegation leader at several Olympics.
He said athletes making their own housing arrangements won't have the same level of protection as those staying at the Olympic village, which comes under the Greek security umbrella.
The United States is sending 550 athletes and a support staff of 300, along with more than 100 federal agents to keep an eye on them, USOC chief security officer Larry Buendorf said last week. While the vast majority of the athletes will stay in the Olympic Village, the NBA stars may stay aboard the Queen Elizabeth II in Piraeus harbor, he said.
The United States also has rented out the American College of Greece, where athletes will train in a complex that has an Olympic-size pool, track and gymnasiums. Many athletes will spend nights in dorms on the campus before their competitions instead of staying in the Olympic Village.
Whether foreign security personnel can carry arms is up to the Greek government, Rogge said.
Greek Public Order Minister Giorgos Voulgarakis has repeatedly said that no foreign security personnel will be allowed to carry weapons. There is widespread speculation, however, of a tacit understanding that athletes from the United States, Israel and other high-risk nations will have armed protection.
In Athens, a training program for Greek security forces featured a variety of mock Olympic crises, including information about an attempt to assassination British Prime Minister Tony Blair, the newspaper To Vima reported Wednesday.