Reporters Wa Lone, 32, and Kyaw Soe Oo, 28, both Myanmar nationals, were arrested in Yangon in December 2017 and later jailed for violating the Official Secrets Act.
Reuters says the charge was trumped up to muzzle their reporting into a massacre of Rohingya men.
The two were convicted of possessing classified information regarding security operations in Rakhine state, from where hundreds of thousands of Rohingya Muslims fled during an army-led crackdown the United Nations has described as “ethnic cleansing”.
But their sentence provoked outcry over media freedom in Myanmar with calls echoing across the world for their immediate release.
In January Yangon’s High Court rejected their initial appeal leaving their fate in the hands of judges at the Supreme Court.
“We are going to appeal this morning,” lawyer Khin Maung Zaw told AFP from the capital Naypyidaw, seat of the Supreme Court.
“We hope they are not going to reject it.”
Under Myanmar law Supreme Court judges hear appeals individually, giving lawyers for the journalists several options.
The process is expected to take several months.
The only other chance of early release comes from a presidential pardon.
Rights groups have heaped pressure on de facto civilian leader Aung San Suu Kyi to use her leverage to secure a pardon.
But she has steadfastedly refused to intervene in the case in favour of the reporters, describing it as an issue for the courts.
At the time of their arrest, the men were probing the extrajudicial killing of 10 Rohingya men at Inn Din village in northern Rakhine state.
The pair insists they were victims of a police set-up.
Testimony during the trial from a whistleblowing officer appeared to validate their claim.
Moe Yan Naing, was initially called as a prosecution witness but stunned the court by saying superiors had ordered police to entrap the reporters.
His breaking of the ranks was extremely rare from a serving member of Myanmar’s secretive security apparatus and he was jailed for a year after giving testimony.
On Friday the ex-policeman walked free after serving his sentence at Yangon’s Insein prison — where the Reuters reporters are also doing their time.
“I’ve never broken any police regulations in my life, but the police regulations are not perfect,” he told reporters as he left the jail.
“Members of the police force are suffering under these,” he said, calling for reform “as part of the transition to democracy”.
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