Luca, who had been detained at Nicosia Central Prison since he was arrested in 2012, lost an appeal at the Cypriot Supreme Court, The Star reported on Friday.
Luca fled South Africa shortly after Jackson's killing and returned to his hometown Limassol, in Cyprus.
His lawyer Sofronios Sofroniou had argued that some of the charges against Luca were six years old and that this could jeopardise his chances of a fair trial. There were also concerns that the South African underworld could endanger his life, it was argued.
An extradition process started after Luca, also known as Luca Smith, was caught in Cyprus in March 2012 and detained by local police.
"But I don’t think I will get a fair trial,” he was quoted as telling the Sunday Times before his arrest. “I am alive because I am not a betrayer."
Jackson, the owner of the Teazers franchise of strip clubs, was shot dead at a house in Edenglen, near OR Tambo International Airport, on May 3, 2010.
A police investigation was launched which revealed hidden aspects of the Joburg underworld and possible links with the subsequent murder of Jackson's attorney, Iaan Jordaan.
Cypriot-born Luca, a former Special Forces soldier who had carried out debt-collecting work for Jackson, had allegedly phoned Gauteng crime intelligence boss Joey Mabasa and confessed to killing him shortly after the murder.