The Italian head coach led the Blues to the Premier League title in his first campaign in charge of the west London side.
Chelsea FC won the Premier League crown with two games to spare after finishing seven points ahead of their bitter rivals Spurs.
However, the defending champions have struggled to maintain their high standards under Conte this term.
Chelsea FC lost 3-1 to Tottenham Hotspur at Stamford Bridge on Saturday evening after Christian Eriksen cancelled out Alvaro Morata’s opener before Dele Alli netted twice in the second half.
The Blues are eight points behind fourth-placed Tottenham Hotspur in the Premier League table to leave Chelsea FC with a mountain to climb in the top-four race.
Conte is coming under pressure at Chelsea FC following a run of five losses in their last seven games in the Premier League.
Former Manchester United defender Neville doesn’t believe Conte will be at Stamford Bridge next term.
“I don’t think he’s going to be here next season,” Neville said on the Gary Neville Podcast. “We’ve thought it for six or seven months.
“And that’s not because we don’t want him here, or we don’t think he’s done a great job, it’s just the nature of the job here. It’s such that when you have a season slightly worse than before, you go.
“It ends up becoming a bit messy, press conferences become the boardroom versus manager, it’s happened here many, many times.
“It has been a successful club over 10 or so years, but in the second seasons, it’s never been great. In terms of the outcome, you can’t complain about what they’ve done here. But the managers who come here know they’ve got a short period of time.”
Chelsea FC have been linked with a potential move to appoint former FC Barcelona manager Luis Enrique and ex-Borussia Dortmund boss Thomas Tuchel.
The Blues signed Ross Barkley, Emerson Palmieri and Olivier Giroud in the January transfer window.
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