David Porter, 34, said he and his brothers – Robert, 37, and Michael, 29 – hope it could yield vital clues about what happened to their mother Jean Hanlon.
Ms Hanlon, 53, a former hospital secretary, who had been living on the Mediterranean island, was last seen alive on a night out four days before her body was found in the sea.
Mr Porter said an appeal on Greek television around the third anniversary of her death in March might bring forward fresh information.
He hopes to make the new appeal alone or with one or both of his brothers.
Mr Porter, a hospital porter from Dumfries, said: "We did a television appeal initially and it worked a bit.
"I was speaking with Michael the other day about doing another and he thought it was a good idea. I hope Robert would be able to take part too.
"It would bring our mother's death to the attention of the public again. Our lawyer has asked for a few people to come into his office. An appeal might be a good way of reaching them.
"It could yield new information. Maybe someone saw or heard something which they haven't told the police but which might be important."
He added he would be calling journalists who worked with Greek television companies to put the idea forward.
Mr Porter last spoke to his mother a couple of days before she disappeared. He said she had been in a good mood after getting a new job.
He also told The Herald the procurator-fiscal in Dumfries had contacted him and he had handed over a copy of the Greek police file on the investigation into his mother's death.
However, it was unclear whether the Crown Office would pay £2500 to have the file translated from Greek, he said.
"We were hoping once it was translated the fiscal might spot something we could take back to Crete, something the authorities there could look at again," he said.
In July last year the authorities in Crete decided not to charge anyone over the death.
Ms Hanlon, from Dumfries, who was divorced, was found dead in the sea off the island's capital, Heraklion.
She had been living on Crete since 2005, working in bars and restaurants in the coastal village of Kato Gouves.
The investigation has been beset by problems and delays. The local coroner initially ruled she had drowned, a verdict that suggested her death was accidental.
However, months later he changed his opinion to declare she had died from a neck injury before her body ended up in the sea. Police identified two suspects – a Greek and a Belgian who were both friends of Ms Hanlon on Crete.
The two, who insisted they were innocent, came under suspicion because of inconsistencies in their statements, but were released after questioning.
Dumfries and Galloway Labour MP Russell Brown said: "The brothers have been very disappointed by the progress in the inquiry. Things seem to have moved on from the death being regarded as accidental, and the authorities now seem to be regarding it as suspicious."
A Crown Office spokeswoman said a meeting between David Porter and the procurator-fiscal for Dumfries and Galloway had taken place and had been facilitated by Mutual Legal Assistance – where investigators can obtain evidence located in one country to assist in criminal proceedings in another.
The spokeswoman added the content of the meeting was confidential.