His father, Alhaji Umaru Mutallab, is a prominent banker well-connected in Nigeria's political world, the BBC's Caroline Duffield reports from Lagos.
In recent months Mr Mutallab is said to have become alarmed about the political views of his son, who is a former engineering student at University College London.
He approached the US embassy in Abuja in November to voice concerns about his son, according to American officials.
The family have told the BBC Hausa service that they lost contact with Mr Mutallab in October, when he was living in Yemen.
He left there for Ethiopia, then went to Ghana and finally Nigeria, US officials have told his family.
How the accused, who had a valid US travel visa, boarded a flight in Lagos to Amsterdam, despite being on a database listing individuals of concern to the authorities, is a key question, our correspondent says.
Anti-terrorist measures in Nigeria's airports are haphazard and corruption among police, customs and security officials is endemic, she adds.
Officials in Washington, speaking on condition of anonymity, told news agencies that Mr Abdulmutallab's name had been added to a security watch-list of more than half a million individuals, known as Terrorist Identities Datamart Environment (Tide).
But there was apparently not enough information to include his name on the smaller Terrorist Screening Data Base, which includes a no-fly list.
It is understood that members of Mr Abdulmutallab's family are travelling to the Nigerian capital Abuja on Sunday to meet police and government officials.
'Nice and polite'
A preliminary FBI analysis has found that the device allegedly found on Mr Abdulmutallab contained the high explosive PETN, also known as pentaerythritol.
Umar Farouk Abdulmutallab's former teacher Mike Rimmer
PETN was used in the device worn by British "shoe bomber" Richard Reid, who is serving a prison sentence for attempting to blow up a Paris-Miami airliner in Christmas week of 2001.
Mr Abdulmutallab allegedly tried to detonate a device using a syringe, but it failed to go off.
The suspect has reportedly told investigators he had links to al-Qaeda and received the explosives in Yemen for a suicide attack, after a month of training.
Mr Abdulmutallab went to the bathroom for about 20 minutes before the incident, court documents say.
When he got back to his seat, he said he had an upset stomach and pulled a blanket over himself, the affidavit continues.
"Passengers then heard popping noises similar to firecrackers, smelled an odour, and some observed Abdulmutallab's pants, leg and the wall of the airplane on fire," the Department of Justice said in a statement.
Dutch tourist Jasper Schuringa, credited with tackling the suspect first, is being hailed as a hero by fans on the internet.
The 32-year-old Dutch filmmaker said when he heard a bang and smelled smoke he felt immediately it was a terrorist attack.
Mr Schuringa added that the alleged bomber had not become aggressive after the alleged bomb failed to detonate.
"He was actually a normal person, he was very scared, he had a very frightened look, he wasn't resisting or anything," he told the BBC.
"I also spoke later to one of the Dutch people who was sitting next to him and they said he was a really nice and polite man. So he was someone you wouldn't expect to commit a crime like this."
Meanwhile, delays have been caused to transatlantic flights after airlines flying in to and around the US tightened security.
Measures include cutting down on hand baggage, extra frisking of passengers at passport control and allowing more boarding time.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.