Some are expected to boycott the proceedings and their hearings will be held in absentia, Peppler said.
The US military held 558 combatant status review tribunals between July 2004 and March 2005 and the panels concluded that all but 38 detainees were "enemy combatants" who should be held. Those 38 were eventually released from Guantanamo.
The military allowed the media to cover previous hearings but this time has adopted more stringent rules, barring anyone without a special security clearance.
The 14 detainees include Khalid Sheikh Mohammed, a suspected mastermind of the September 11 attacks who was captured in Pakistan in March 2003, and other alleged al-Qaeda figures.
Legal experts have criticised the US decision to bar independent observers from the hearings and The Associated Press news agency filed a letter of protest, arguing that it would be "an unconstitutional mistake to close the proceedings in their entirety".