Authorities in the gulf state, where Patterson, 24, worked as a primary school teacher are said to be conducting DNA testing on the body to confirm an identification.
Patterson disappeared early Saturday morning after last being seen leaving a club at a luxury hotel in Doha. Her boyfriend, James Grima, sounded the alarm on Facebook, and her body was found several hours later, so badly burned it could not be visually identified.
Patterson's mother, Alison Patterson, flew to Qatar earlier this week to "fight for justice" for her daughter.
And while she described the waiting for positive identification as "extremely stressful," Brian Roake, Lauren's uncle and Alison's brother, spoke well of the Qatari authority's response.
"We have had a high-level meeting with senior officials in Qatar who are leaving no stone unturned," Roake said. "It has obviously been an extremely stressful time waiting but we know the authorities are doing everything that they can."
Qatar's Interior Ministry released a statement Wednesday saying that suspects had been arrested, but declined to reveal the number or nationality of those detained.