The big midfielder has been excellent this season.
Payet and Lanzini have been two of the Hammers' stand-out flare players in a season which has seen Slaven Bilic's side reach an FA Cup quarter-final and mount a serious challenge to finish in the Champions League places, with the Irons sixth ahead of the final two league games.
The Senegalese defensive midfielder, with 31 Premier League starts so far this season, has played a massive role in that, shielding the back four and giving his more advanced team-mates at a platform for which to build attacks.
And the donkey work has not gone unnoticed by Cottee, who says he perhaps deserves as much credit as his midfield partner in crime Mark Noble.
"We have spoken about Mark Noble so many times this season, so maybe we should mention his midfield partner Cheikhou Kouyate who is a vital part of the team," he wrote in London 24.
"Every team needs a player like Kouyate who can allow Noble to get further forward and win the ball, so players like Dimitri Payet and Manuel Lanzini can get on to the ball."
Next up for Bilic and co is the visit of Swansea City, fresh from a 3-1 win over Liverpool, but the Irons have won their last two games by an aggregate score of 6-1, and Cottee backs another convincing victory in East London this weekend.
"We have Swansea coming on Saturday and though you might have thought they were on the beach, they showed by beating Liverpool that they are a decent side," he added.
"The way we are playing though, I can’t see anything except a win and I will go for a big 3-0."