David Miller, 24, and Hannah Witheridge, 23, were found naked and beaten to death early Monday near a beachside bungalow on the island, a diving hot-spot near Koh Phangan in the Gulf of Thailand.
A bloodied hoe was discovered 35 metres (yards) from the murder scene.
"Three male Myanmar migrant workers are under police detention for investigation," southern regional police commander Panya Maman told AFP, without providing any further details.
His comments came after UK media reports said police were seeking a British man who had been travelling with Miller in connection with the killings.
Panya could not confirm Thai television reports that police had seized an iPhone and blood-stained jeans after raiding rooms used by the Myanmar suspects.
Thai authorities frequently accuse migrants from Myanmar and Cambodia of committing crimes in the kingdom, where they make up a vast, poorly-paid and low-status workforce.
The bodies of the victims, who arrived in Thailand on August 25, are due to arrive in Bangkok later Tuesday for forensic tests, said local police official Jakkrapan Kaewkhao.
AFP