The Sun says Brunt, 33, took aim at his manager's tactics in a furious dressing-room rant following Saturday's 2-1 home defeat by Huddersfield.
Brunt, who has more than a decade of service at The Hawthorns, lashed out at team-mates after a result that left them seven points from safety at the foot of the table.
The midfielder came off the bench to create Craig Dawson's consolation goal.
Brunt accused players of under-performing and lacking desire and effort in full view of his boss, before rounding on Pards.
The Northern Ireland star openly questioned his tactics, claiming Pardew got the formation wrong.