Advani also pointed out that Osama's hideout in the garrison town of Abbottabad was constructed when former President Parvez Musharraf was "in total command of the situation" Pakistan.
In his latest blog, the veteran leader said the military ruler, when came for Agra summit in 2001, told him "a white lie" about Dawood when his extradition sought.
The BJP leader wrote: "It was the same kind of lie that the Pakistanis have been feeding to Americans all these years about Osama."
Recalling Musharraf''s first visit to India on the invitation of then Prime Minister Atal Behari Vajpayee, the BJP leader said the General''s face "suddenly turned red and unfriendly" when Dawood's extradition was demanded and he "replied assertively" that "Dawood Ibrahim is not in Pakistan."
Advani, the then Home Minister, was the first to call on Musharraf at the Rashtrapati Bhavan where he had been put up.
"Later, one of the Pakistani officials who was present during the meeting, said to me, ''What our President said about Dawood Ibrahim on that day was a white lie," Advani said recalling the conversation between him and Musharraf at Rashtrapati Bhavan on July 14, 2001.
Musharraf, who was "hardly able to conceal his discomfort", remarked "''that is small tactics'' (demand for Dawood''s handing over)," Advani said narrating the sequence of discussion between the two in which five Indian officials were seated on one side and five from Pakistan on the other.
"I could sense a sudden change in the atmosphere in the room."Advani said Musharraf''s first response was positive when he suggested an extradition treaty between India and Pakistan.
But, the situation got suddenly changed when Advani demanded the handing over of Dawood, who is the prime accused in the 1993 Mumbai serial bomb blasts case and "who lives in Karachi", to India even before both the nations conclude a formal extradition treaty.
Quoting reports, Advani said the three-storied hideout for Osama and his family in Abbottabad was constructed in 2005.
"It would thus be reasonable to believe that the decision was taken when General Musharraf was in total command of the situation in that country," he added.