The trial of Thanyanat Sama-arphat and Sangdao Wongtrakool began on Tuesday. The judgement could be delivered on March 27, the Phnom Penh Post reported on Wednesday.
Ms Thanyanat was arrested at Phnom Penh international airport on May 4 last year, allegedly with six packages of cocaine weighing more than one kilogramme, following a tip-off from Thai officials.
Cambodian police later arrested Ms Sangdao at a hotel in the Cambodian capital. She was allegedly to receive the drugs.
The two defendants have denied the charges.
The Cambodian anti-drug agency charges the cocaine was from Brazil and the defendants planned to smuggle it into Thailand from Cambodia.