The Italian head coach was appointed as the permanent Chelsea FC boss in May 2016 following their tenth-placed finish last term.
The Blues won the Premier League title with two games to spare last season but lost 2-1 to Arsenal in the FA Cup final at Wembley.
Chelsea FC were looking to defend their title for their first time since 2006 but the Blues are a staggering 28 points behind Manchester City.
The west London side lost 3-1 to bitter rivals Tottenham Hotspur in the Premier League at Stamford Bridge to end their 28-year unbeaten run at home.
Former Arsenal striker Wright pondered whether Hazard or Willian could contemplate a potential summer move if Chelsea FC sack Conte at the end of the season.
“Are Hazard or Willian going to stay? Are they ready to go again with another manager? Are they going to give the new manager players to challenge?” Wright told BBC Radio 5 Live. “That’s the problem.
“Conte feels he didn’t get the players to challenge Man City. He has been proven right.”
Chelsea FC are in fifth place in the Premier League table and eight points behind Tottenham, who occupy the final Champions League spot.
The west London outfit can take on Southampton in the FA Cup semi-final with a place in the Wembley showpiece up for grabs.
Chelsea FC were 2-1 winners against Leicester City in the previous round to set up a meeting with the Saints.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news