Ten-man Chelsea suffered their second successive defeat in the Premier League following last Wednesday’s shock 3-0 loss at home to Bournemouth.
Tiemoue Bakayoko was sent off in the first half and despite Eden Hazard cancelling out Troy Deeney’s opener after the break, the Blues conceded three goals in the final 10 minutes.
Chelsea’s next fixture is against bottom-of-the-table West Brom next Monday.
Carragher was asked by Sky Sports’ Monday Night Football presenter Dave Jones if he thinks Conte will still be in charge for that clash.
And the Liverpool legend says it is possible the Italian could be on his way before then.
“There’s a good chance he could go before then,” Jamie Carragher said.
“Not just because of how Chelsea are playing of late or tonight, but because of Chelsea’s history of changing managers when the club fear they’re not going to make the Champions League.
“I think they did it with (Andre) Villas-Boas, (Roberto) Di Matteo, I think with (Jose) Mourinho as well. I think actually they were even worse than that with Jose.
“Antonio Conte said before the game ‘I want the owner and the board to come out and back me’.
“Well that’s never going to happen because Roman Abramovich hasn’t come out and spoken about anything in 10, 15 years, whatever it is he’s been at the club.
“So that’s not going to happen and it’s certainly not going to happen on the back of tonight.”