If former Reuters journalist David Fox, 55, is handed a one-year sentence, it would include time already served, meaning he could be released from jail in a matter of months.
Prosecutors will recommend a jail sentence for Australian businessman Giuseppe Serafino, 48, who was detained before Fox and led police to the journalist, at a later hearing.
The pair are charged with using, possessing and transporting hashish after allegedly being caught in possession of small amounts of the drug in October.
The former Reuters journalist covered wars and disasters in countries including Bosnia, Rwanda and Iraq.
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At Thursday's hearing in the Balinese capital Denpasar, prosecutor Erawati Susina said that Fox's actions were "against the government's programs which are aimed at eradicating illicit drugs".
Under Indonesia's tough anti-drugs laws, they could face several years in jail but Susina said prosecutors were seeking a lenient sentence as Fox was a first-time offender and had admitted his wrongdoing.
Judges do not have to follow prosecutors' sentence recommendations but they often do.
Fox was later arrested and police found 10 grams of hashish in his pocket and at his house, along with smoking equipment.
Indonesia has some of the toughest anti-narcotics laws in the world but the pair will escape the death penalty as they have not been charged with trafficking.