Hannah Witheridge, 23, and David Miller, 24, were found dead on a beach on the island of Koh Tao on Monday.
Two British men who spent time with the victims in the days before they died are now in "police care" in Bangkok.
Police said the men had not been formally detained or arrested but had been prevented from leaving the country and could be questioned.
The men, believed to be brothers, are not in custody but are being escorted by police in Bangkok, Thai police told the BBC.
One of them was questioned on Monday shortly after the bodies were found, but was later released.
A senior officer said the renewed focus on the two men was the result of new forensic evidence.
The term "possible suspects" is being used because declaring a suspect is an official judicial process in Thailand.
No official suspects have yet been declared in this case.
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