The defending Premier League champions have struggled in the 2017-18 season following a disappointing summer transfer window.
Conte was left frustrated after the Italian head coach missed out on some top targets, including Romelu Lukaku and Alex Sandro.
Chelsea FC suffered their first loss to Tottenham Hotspur at Stamford Bridge since 1990 when the Blues slumped to a 3-1 defeat.
The Blues are eight points behind fourth-placed Tottenham in the race to secure a Champions League spot.
Conte’s men are facing the possibility of a second season in three campaigns without Champions League football.
Former Arsenal striker Wright believes Conte has struggled with his lack of power at the defending Premier League champions this term.
“I believe Conte may have thought winning the league may have given him more leeway with the Chelsea board,” Wright told BBC Radio 5 Live.
“I didn’t think it would have bothered him to the extent it has. He has complained about certain things throughout the whole season.
“His personality on the touchline has changed. He looks like he is waiting to go.”
Chelsea FC suffered a 4-1 loss to FC Barcelona in the Champions League round of 16 last month.
The Blues signed Everton playmaker Ross Barkley, AS Roma defender Emerson Palmieri and Arsenal striker Olivier Giroud this term.
Conte was appointed as Guus Hiddink’s replacement in May 2016 and led the Blues to the Premier League title in his first season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news