Mr. Shannaq was a roommate in Alexandria of hijackers Hani Hanjour and Nawaf Hamzi who crashed American Airlines Flight 77 into the Pentagon on September 11.
US authorities are investigating a suspected visa scam which may have allowed 71 people - including some with links to the 11 September attackers that the US blames on the al-Qaeda network - to have entered America illegally. At least one former employee of the US embassy in Qatar has been questioned about alleged bribery, reports say.
The FBI has detained 31 people suspected of entering the US with visas illegally obtained at the embassy, US State Department spokesman Philip Reeker said.
He said that investigators were still looking for 29 more people who had received suspect visas.
Six others are believed to have left the US and five others believed to have entered the US illegally are spouses or children of a visa holder, Mr Reeker said.
Other officials, quoted by the AFP news agency, said that the investigation dubbed "Operation Eagle Strike" had identified 39 Jordanians, 28 Pakistanis, three Bangladeshis and one Syrian who had received visas from the embassy in Doha between July 2000 and May 2001.
The officials said those who had been detained since 24 June were 25 Jordanians, five Pakistanis and one Syrian.
Three are believed to have links with the 19 hijackers who took part in the 11 September attacks, the officials said.
The three include Ramsi Al-Shannaq, a Jordanian who has admitted being a room-mate of two of the hijackers.
He was arrested in Baltimore on 24 June and charged with illegally obtaining a US visa.
At a court hearing in Baltimore on Wednesday, Assistant US Attorney Harvey Eisenberg said that Al-Shannaq, 27, had been denied visas four times before paying $13,000 for an illegal one.
Mr Eisenberg said Al-Shannaq was part of a bribery ring that involved pay-offs of more than $13,000 per person.
In a little more than two weeks, 31 who obtained the visas in Qatar have been rounded up, including the three suspects. One is Al-Shannaq, who investigators believe roomed in Alexandria, Va., last summer with the two eventual hijackers. The FBI was tipped off last November that he had obtained the visa for $10,000 in Qatar. He was arrested June 24. Eisenberg said he was part of the bribery ring that involved payoffs of more than $13,000 a person. The two other detained foreigners suspected of links to terrorists were not identified. One of the embassy employees under investigation is an American citizen currently living in Virginia. He has hired a lawyer and is not cooperating with authorities, who are reviewing his finances for evidence of bribes. The other now lives in Jordan. Together, according to one official, they processed visas at the Doha embassy for about 14 months.