Pacteau, 21, was jailed for a minimum of 23 years in September after admitting bludgeoning Ms Buckley to death with a spanner in April.
He then attempted to dispose of the 24-year-old’s body in a vat of chemicals.
Trial judge Lady Rae said he had carried out a “brutal, senseless and motiveless attack on a defenceless young woman”.
Pacteau’s case is to be heard in front of three appeal judges at the Court of Criminal Appeal in Edinburgh aon December 4.
Ms Buckley, from Ireland, who was studying at Glasgow Caledonian University, was in the Sanctuary nightclub in the city when she met Pacteau.