Blackburn Rovers refused to sell N'Zonzi to the Hammers, having fallen out with Sam Allardyce following his sacking.
That left the door open for Pulis to snap him up and Stoke duly grabbed the enforcer for a bargain £3million in the summer.
Pulis said: "Sam said we should get him if we could.
"I'm glad for the advice because he's a top player. If he keeps improving he can play for any of the top four teams. He's been outstanding - one of the best signings we've made."