The French attacking midfielder has been at Upton Park for less than a season, but he has quickly developed a reputation as one of the finest players to represent the London side in recent times.
Payet has put in a series of mesmeric performances, and he has quickly become Slaven Bilic’s side’s main creative force.
“Already he has done things that have put him into cult status,” Ashton said.
“That’s what West Ham fans love, things that shock you and you’re in awe of and he has done maybe five or six special moments like that this season.
“That’s why West Ham should build their team around him. He has that affinity with the fans already and loves the pressure of being the big player at West Ham which is something Di Canio had as well.”
Payet has scored 12 goals and made 11 assists during his first season in English football.
The former Marseille man has dazzled, with his natural flair in possession quickly catching the eye.
Payet’s wonderful form has been a major reason behind West Ham’s excellent season, where they have managed to challenge for a top four place in the Premier League.
The Hammers are currently in sixth place in the top flight standings, but they are hot on the heels of the likes of Arsenal and Manchester City.