Police investigating the deathsof David Miller, 24, and Hannah Witheridge, 23, are trying to trace a man who left Koh Tao the day their bodies were discovered on the island, the BBC reported.
It said the man is believed to be in the capital Bangkok, and that police believe at least three men were involved in attacking the young Britons.
Police colonel Kissana Phathanacharoen refused to comment on the new lines of inquiry.
Mr Miller, from Jersey, and Miss Witheridge, from Great Yarmouth, Norfolk, were found with severe head wounds on the island’s Sairee beach on September 15.
A bloodstained garden hoe, believed to be the murder weapon, was found nearby.
Post-mortem examinations revealed that Ms Witheridge died from head wounds while Mr Miller was killed by severe blows to the head and drowning.
Around 150 police have been posted to the island but are so far apparently no closer to finding the killer.
A spokesman for the Royal Thai Police said on Monday the force was looking into claims the pair had a row with a Thai man in a bar before they were killed.
On Sunday Mr Phathanacharoen said officers were investigating new evidence suggesting the murders might have been due to “sexual jealousy”.
He said: “We have discovered fresh evidence which could lead to a new suspect who may have had a relationship or one-night stand with Hannah or one of her friends or David the night before they were killed.”
Mr Miller’s father Ian said earlier this week he believes his son stepped in to help Miss Witheridge during an altercation.
He told the Daily Mail: “It has become clearer and clearer that it is quite likely David was stepping in to help a girl who was in trouble.”
Last week police said they were looking for more than one suspect following unconfirmed reports that the DNA of two Asian men had been found on Ms Witheridge’s body.
A group of Burmese migrants who were interviewed by police after bloodstains were found on their clothes have been eliminated from inquiries.
No matches were found between them and DNA found on Ms Witheridge and a cigarette butt at the scene.
Police had previously said they were looking for three Westerners who were seen playing a guitar near Sairee beach.