A story in The Independent claimed Ashley made the comments while out drinking on Thursday night, supposedly making a throat-cutting gesture as he discussed Pardew's future.
"I spent time up there, and the club deserve better," Barton said while appearing on BT Sport.
"It just seems typical of the way things are done up there. If I'm the manager, I do not wanna be hearing or reading that."
Barton, 32, spent four years on Tyneside before joining Queens Park Rangers in 2011.