Derek Kang told AFP that his client Oliver Fricker, who is currently serving his jail term, formally tabled the appeal for a lower jail sentence last Friday.
"That is correct," Kang said when asked if his client had lodged the appeal.
Fricker, 32, was also sentenced to three strokes of the cane last month in the Singapore district court after he pleaded guilty to trespass and vandalism which are considered serious offences in the city-state.
Kang said he was not aware if his client has been caned.
Singaporean authorities did not immediately respond to AFP queries on the matter.
Under Singapore's tough laws, a minimum three strokes of the cane is mandatory for vandalism. The punishment entails being struck with a wooden stick on the back of the thigh below the buttocks, which can split the skin and leave lasting scars.
Prosecutors said Fricker and a British friend visiting Singapore broke into a subway depot and spray-painted two carriages before dawn on May 17 as part of a premeditated prank.
Singapore has launched an international hunt for the 29-year-old Briton, Lloyd Dane Alexander, who allegedly planned the act but left the city-state before he could be caught, leaving Fricker to face the consequences.
The city-state, a close US ally in a predominantly Muslim region, says its metro subway system is believed to be a target of Islamic extremists.
Singapore's vandalism laws first became global news in 1994 when an American teenager, Michael Fay, was caned for damaging cars and public property despite appeals for clemency from the US government.