It is understood Blues owner Roman Abramovich won't sack Conte right now. But Wright believes his time will be up at the end of the season.
He said on Sky Sports: "No I do not (think he will still be at Chelsea next season).
"When you see him talking about and actually mentioning the length of his contract, saying, 'I have 18 months left and I am not going' it is almost as if he is saying, 'if they want me to go, they are going to have to get rid of me'.
"It is a sad situation that they now find themselves in because I cannot understand that Chelsea would promise him something else for him to be getting so angry like he is.
"I genuinely believe it is because Chelsea have stuck to their guns and said, 'no, we are going to buy the players'.
"So no, I do not think he will still be there next season as the people upstairs have now had enough."