It is believed Ms Mc Laughlin arrived in the region on Sunday and attended a party on Palolem beach on Monday night before her body was found near Deobag Beach early on Tuesday morning.
Her body was unclothed and she had marks on her head and face, it has been reported.
However, another person claiming to know her tweeted to say her body had been found in “dumpster” behind the hotel.
Miss Patterson's mother Alison took to Facebook to thank people for their support and pay tribute to her daughter.
She had been living and working in Liverpool having attended the city's John Moores University before setting off in February.
The Times of India reported she was discovered in the popular tourist Canacona area in the south of the Indian state.
Supt Sammy Tavares told reporters that they had arrested a suspect: "He has confessed to raping the victim and later killing her in order to hide his identity." Residents of the community where Ms Mc Laughlin’s body was found are planning a vigil in her memory.