The billionaire businessman made the comments while out drinking on Thursday night, according to The Independent, supposedly making a throat-cutting gesture as he discussed Pardew's future.
"He's got one more game," Ashley is quoted as saying. "If we lose against Stoke on Monday night then he's gone. I have had enough.
"Dead. Finished. Over. One more game then that's it. What would you do? I have spent a lot of money on that club, it's cost me a lot. I won't put up with it any more. Honestly, answer me, what would you do? One more loss and he's gone, he's over, finished."
The comments have been dismissed as being tongue-in-cheek by Ashley's legal team, though Pardew is yet to receive a public vote of confidence from his boss.
Newcastle currently sit bottom of the table with just one win in 13 Premier League games.