Omar, 34, Osama bin Ladens fourth-eldest son, was travelling with his British wife Zaina al Sabah from Doha, and they asked to be sent to Turkey, the sources said to Reuters.
The couple, who lived in Egypt for several months in 2007 and 2008, were previously denied entry to the country in 2008.
Omar bin Laden broke with his father in 2001 after living in Afghanistan for much of 1996 to 2001.
In an interview with Reuters in 2010, Omar said he was working with Saudi Arabia and Iran to end his separation from a group of brothers and sisters that dates back to the chaos in Afghanistan following the al Qaeda attacks of Sept. 11, 2001.
Omar said bin Ladens children were trying to be "good citizens of the world" but suffered from the lack of a father and the stigma of being the al Qaeda leaders children. None were part of al Qaeda, he said at the time.
"We are working with the Iranian government and with the Saudi government at the moment to have my mothers children and grandchildren join us," he said.
Osama bin Laden was killed at his Pakistani hideout by U.S. commandos in 2011 in a major blow to the militant group which carried out the Sept. 11 attacks.