Kirsty Jones's murderer has still not been found
Twenty-three year-old Kirsty Jones, from Brecon, was found dead in the northern city of Chiang Mai on August 10, 2000.
On Friday, Thai police have now said they expect the case to be solved "very soon".
Mike Gooding, a friend of Ms Jones's family, says they are hopeful the case will soon come to a conclusion.
The British authorities in Thailand have been kept informed of progress by the Royal Thai Police and it is expected that a representative of the British Police will meet Thai Police next week.
Andrew Drummond, a freelance reporter in Thailand, said nobody had been arrested in the case yet, but any development in this case is significant.
He added that British officials are cautiously optimistic.
Prime suspect
In January, the investigation was reopened and DNA tests were carried out from the crime scene by British detectives.
Eight men suspected of the murder were cleared after the test results of DNA tests were returned to detectives.
On Friday, police said an end to their search was near, but did not say what new evidence had led them to their prime suspect.
"Currently, we have a prime suspect and soon the case will be completely solved, very soon," said Colonel Dinai Boonruang.
He added that two Thai men had been subjected to DNA tests on Thursday so they could be witnesses in the trial.
Jetsada Viriyasakul, 28, and Cha Kesrachai, 26, are not believed to have killed Jones, but are thought to have been near the scene of the murder in Chiang Mai, which is 360 miles north of Bangkok.
Colonel Boonruang declined to comment on reports in a local newspaper that police believed the two men were very close to the killer and helped him destroy evidence.
During a visit to London by Thai Foreign Minister Surakiart Sathirathai in January, Foreign Minister Jack Straw said the UK government was very keen to see the killers caught.
Welsh help
A pair of detectives from Dyfed-Powys Police had been brought in to assist Royal Thai Police's floundering hunt, re-launching the inquiry for their man in September 2001.
They flew to the murder scene and later returned DNA evidence from the sarong used to strangle Ms Jones, and from other items in her £10-a-night Aree guesthouse room, for analysis in the UK.
In the initial investigations into her death Thai police arrested the hostel owner Andrew Gill, 33, after releasing a number of other suspects.
He had always vehemently denied any involvement in the death of the Liverpool University media and English graduate and was subsequently released without charge.
Their handling of the case has been strongly criticised by Ms Jones' parents Sue and Glyn, still angry no-one has been brought to justice.