Analysis of the samples which are understood to have been collected by Thai officials is due to take several days and the results will then be sent to the UK for comparison.
Cold case detectives investigating the death of the unknown woman, who was found in 2004 near Pen-y-ghent, confirmed at the end of last week that they have received a possible name and inquiries are ongoing.
Her half-naked body was found by walkers on the Pennine Way and investigators believe she may have been killed and transported to the stream, possibly by a 4x4 vehicle. A cause of death has never been established and a 2007 inquest recorded an open verdict.
Reports added that a Press conference in north-east Thailand revealed a family had come forward to say the missing woman could be their relative.
They said she married a British man in the 1990s and moved to England and that they had not heard from her since 2004, according to the reports.
They produced photographs of the missing woman alongside an artist’s impression released by the British police which was published as part of the attempt to trace her.
Last year, North Yorkshire Police said officers believed the woman was a “Thai bride” who came to this country after marrying a local man.
Advanced tests on her hair revealed she lived in north Lancashire or south Cumbria.
A North Yorkshire Police spokesman said: “The Cold Case Review Unit has received a name regarding the unknown South East Asian woman who was found dead on Pen-y-Ghent in 2004.
“Inquiries are ongoing to establish the identity of the woman.”
Speaking back in October, Adam Harland, the manager of the North Yorkshire and Cleveland Police cold case review team, said: “[It is possible] she is a lady who has taken up a relationship with a white gentleman, and come back to the UK.”
The force appealed for anyone with information to call 101.