The West Ham icon says you can see why the comparison is being made.
The Frenchman moved to east London from Marseille this summer and has begun tremendously, particularly impressing on Monday night as Cottee and the class of '86 watched West Ham beat Newcastle United 2-0.
And Cottee told London 24: "Dimitri Payet had a great game and you can see why people are saying that he is the best player at Upton Park since Carlos Tevez.
"Some of the tricks he was doing were great and he reminded me of Alan Devonshire in the way he can create something from nothing."
Payet's phenomenal start to life at West Ham is certainly worthy of all the praise it gets and will continue to get if the Frenchman's form carries on at this rate.
The question has to be asked of other Premier League clubs who didn't move for the 28-year-old, who was clearly available this summer.
There seems to be a sense that 21/22 year-olds are the only way to go - at two or three times the cost. But the West Ham man has already proved his experience to be invaluable. It's about keeping it up, of course, with the Hammers knowing all too well what it's like to see a player dip in form (see Alex Song).
But the Tevez comparisons certainly aren't wide of the mark.