Prosecutors are calling for the 16 to be charged with belonging to a terrorist organisation, the Dogan news agency reported.
On Thursday, Interior Minister Efkan Ala said seven people had been arrested over Tuesday's attack which the authorities have said was the work of a Syrian bomber from the Islamic State group.
Ten German tourists were killed and another 17 people wounded in the bombing in the historic centre of Istanbul near the Blue Mosque and the Hagia Sophia, the towering former Byzantine church that is now a museum.
The 16 suspects, whose nationalities were not disclosed, are said to have links to the IS group and the court must decide whether to charge or release them.
Ankara has often been criticised by its Western allies for not doing enough to combat IS jihadists who have seized swathes of territory in neighbouring Syria as well as Iraq.