Allardyce wanted the French midfielder to join him at West Ham but the transfer was denied by the Ewood Park board following a fall-out between Allardyce and the club after his sacking.
N’Zonzi, 23, will come face-to-face with his former manager at Upton Park on Monday as the Hammers face Stoke and Pulis knows it could have been a different story had Allardyce got his way.
"I spoke to Sam about him a while ago and he felt Steven will be a top player who hasn’t realised his potential yet," Pulis told reporters.
"He had wanted to sign him but I think that was being blocked because of his relationship with Blackburn at the time. But having worked with him, 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 or five teams."
Stoke could move into the top half of the table with a win and Pulis believes that N’Zonzi and his team-mates will have to be their best to beat a West Ham side that are flying high in the league and eyeing fifth spot.
|SUCCESS FOR STOKE?
|20/1||Stoke are 20/1 to beat West Ham 2-0 with bet365|
The Potters have only managed two victories so far this season but Pulis has been impressed with the former Amiens midfielder, but thinks he still has room for improvement.
"He’s very good in the air, his mobility is excellent as well and it is just getting him more disciplined in the team structure. We also feel he can score more goals," Pulis added.
"He’s that good he should be scoring goals. He’s been outstanding for us – one of the best signings we’ve made at this football club. He has real potential to be a top player."
N'Zonzi could decide to play for Congo in the Africa Cup of Nations in the New Year, but Pulis says he will not influence his player's decision in an attempt to avoid losing him for the duration of the tournament.
"I’ll leave the international stuff to Steven. I think when nationalities come into play you have to leave it to the player to decide." Pulis added, before joking: "But if he picks Congo I’ll never speak to him again!"