Pereira clashed with fans at the final whistle at Molineux, having to be dragged away after exchanging words.
However, The Sun says chairman Jeff Shi is fully behind the manager, having given him a new contract just three weeks ago.
The Burnley defeat leaves Wolves firmly inside the bottom three and also six months since last winning at home.
Wolves’ next game is on Wednesday against Chelsea in the Carabao Cup.