According to The Sun, the Frenchman has had a row with Slaven Bilic and now wants to leave the Hammers, and Wright insisted that, despite his importance to the team, the club must get him off their books as soon as possible, and suggested that the saga may ultimately have a positive impact on the rest of the squad.
West Ham United's Dimitri Payet
Though Payet was sensational for the Irons last season, it is arguably fair to say that his moments of brilliance have been considerably less frequent this term and his general play has been underwhelming.
"He's obviously got a massive attitude problem. I'd get him out now and get as much as you can for him. He doesn't want to be in the fight with his team-mates," he told The Sun's Football Podcast.
"His body language has been terrible since the start of the season. You don't want someone like him around the players.
"It's disgraceful behaviour. It could end up galvanising the team. Fans will want him out."
West Ham United manager Slaven Bilic
Therefore, it may perhaps make sense for West Ham to cash in on him now as a continuation of that form will surely see his value fall by the time the summer window opens, especially as he will be 30 years of age by the time he can move on.
But, on the other hand, it will probably still be less than ideal for West Ham to let Payet go no matter how detrimental him staying would be to the mood within the squad.
On his day, Payet is one of the Premier League's best players, and finding an adequate replacement will be difficult enough before you even factor in that the January window often appears to be much more difficult to do significant business in.