Senegalese-born Vieira was a hero to youngsters growing up in the African country when he was at the peak of his playing career.
And Kouyate said: “People started comparing me to him when I started playing in Belgium which was an immense pleasure. He was a fantastic player and a role model for us Senegalese.
“He made us dream and aspire to do similar things. I know it will be tough but it’s up to me to deserve the comparison.”
Kouyate admits he found those early years in Belgium tough, saying that he had wanted to return to Senegal and stop playing the game.
He said: “I was completely on my own. I saw nobody. But my grandmother, my Mum, the president of my club were on the phone and all told me to stay put.”
Former Anderlecht team mate Romelu Lukaku and Mo Diame also gave advice when he considered joining the Hammers.
And another Sengalese El Hadji Diof told him: “Sam Allardyce will try to make you a better player than I was and that my game would improve under him.”