The Embraer Phenom 300 jet with four people on board was flying from Milan's Malpensa airport to Blackbushe airport in southern England when it crashed at a nearby car auction site. All died in the crash.
It was not immediately clear how the victims were related to the late al Qaeda leader, whose family is one of the most prominent business dynasties in Saudi Arabia.
"We do believe three of the deceased to be the mother, sister and brother-in-law of the owner of the aircraft, all of whom are from the bin Laden family, but formal post-mortem examinations are ongoing," Hampshire Police said in a statement.
Media reports said the victims included bin Laden's half-sister along with her husband and mother. Saudi-owned al-Arabiya television named those killed as Sana' Mohamed bin Laden, her husband Zuhair Hashem and Sana's mother, Raja' Hashem.
The plane's Jordanian pilot was the other person on board, al-Arabiya said. British police said the three passengers were travelling to Britain for a vacation.
Osama bin Laden, the accused mastermind of the 2001 attacks on the United States, was killed by US special forces in a raid on his hideout in Pakistan in 2011.