His wife said, however, that he was denied a British residency request this year after officials there said he had demonstrated continuing loyalty to his father.
Omar Osama bin Laden - one of the al-Qaida leader's 19 children - arrived in Madrid Monday on a flight from Cairo to Casablanca, Morocco, an Interior Ministry official said.
He had been traveling on a Saudi passport, and remained at the airport Tuesday while the ministry considered his request for Spanish asylum, the official said on condition of anonymity in line with ministry policy.
The official did not know on what grounds asylum was being sought. The ministry has 72 hours to make a decision, and the petitioner has a right of appeal.
Omar Osama bin Laden caused a tabloid storm last year after marrying Jane Felix-Browne, 52,who has since taken the name Zaina Alsabah. The couple later said they were planning a 3,000-mile horse race across North Africa next year to draw attention to the cause of peace, but the plan was downgraded to a desert horse race within Egypt in light of the difficulties of obtaining permission to cross borders in North Africa.
Alsabah said in May in Cairo that Omar Osama bin Laden had been denied a British residency request. She showed The Associated Press a statement from the couple's legal firm quoting a British consular officer as saying his residency in Britain would cause public concern and would not be "conducive to the public good."
The British official is cited in the letter as saying that "statements made during recent media interviews indicate evidence of continuing loyalty to your father, who is ultimately held responsible for the London bombing" on July 7, 2005, that killed 52 people on three subway lines and a bus.
Omar Osama bin Laden had declined to directly condemn his father or the Sept. 11 attacks in media interviews, instead condemning all violent acts and saying simply that he had a different approach to problems than his father.
Osama bin Laden is believed to be hiding in the Pakistan-Afghan border region.
Omar Osama bin Laden had moved to Afghanistan with his father in 1996 after living with him in Sudan, and trained at an al-Qaida camp. But Omar has said he hasn't seen his father since he left Afghanistan in 2000 and returned to his homeland of Saudi Arabia.
He has refrained from publicly criticizing his father, saying Osama bin Laden is just trying to defend the Islamic world.