The 49-year-old Brazilian coach, who led Persepolis to title in the 2023-24 Iran Professional League, has not extended his deal with the Iranian club.
Media reports suggest that Vieira has negotiated with Buriram.
Buriram United has played at the top level of Thai football for the majority of its existence and competes in the Thai League 1.
The club was founded in 1970 as PEA FC (Provincial Electricity Authority Football Club) before being reformed as Buriram PEA and Buriram United in 2010 and 2012, respectively.