The agency, whose investigation has led to frustrating false trails, is expecting to make the arrests in the next few weeks, said Newsweek magazine, quoting an unnamed source. "This thing involves husbands and wives as well as children as young as 12," the source said.
In remarks that may be intended to increase pressure on the bombers, the source reportedly said several people involved in the bombing had been co-operating with federal investigators in order to win lighter sentences.
The FBI is under intense pressure to show that it is making progress in its massive investigation into the attack, in which 168 people died after a fertiliser bomb was detonated outside the Alfred P Murrah federal building in Oklahoma City on 19 April. So far, it only has two suspects, Timothy McVeigh and Terry Nichols.
The demand for results has produced a number of optimistic-sounding leaks to the media from within the investigation, including reports that Michael Fortier, an ex-Army friend of Mr McVeigh's, has told investigators that only days before the bombing, he and Mr McVeigh cased the building, which is due to be brought down by an implosion tomorrow.
The Los Angeles Times yesterday said a source had revealed that Mr Fortier, 26, told the FBI that he travelled with Mr McVeigh to Oklahoma City from Kingman, Arizona, to survey the building as a potential bombing target. Posing as job applicants, they inspected the federal offices.
However, these remarks are being treated with some scepticism, as Mr Fortier has proved inconsistent in the past. After the bombing, he said on televisionthere was no evidence his friend planned the attack.
Federal agents are also looking at a white supremacist group in Oklahoma that they believe Mr McVeigh visited before the bombing. The heavily armed community of about 75 people is headed by a Canadian, Robert Millar, 70, known as "grandpa" to his followers.