'As soon as Chelsea's hierarchy feel they could miss out on the top four, that is when they will feel they can make a change.'
Jamie Carragher doesn't think Maurizio Sarri has time to implement his tactics properly at Chelsea after the west London club registered their fourth away defeat in a row.
Chelsea slipped to sixth spot in the Premier League table after the champions thrashed them 6-0 at the Etihad on Sunday.
The Blues haven't been able to score an away goal this year and Carragher says he won't be surprised if Sarri was replaced at the Stamford Bridge helm before the end of the season like they did when replacing Luiz Felipe Scolari with Guus Hiddink, and Andre Villas-Boas with Roberto Di Matteo.
"The problem for Sarri is that Chelsea have had success changing managers midway through the season in the past," the Liverpool great told Sky Sports: "There were managers in the past that tried to implement a certain type of football at the club [Scolari and Villas-Boas].
"Chelsea weren't in disastrous positions in the league at either time, but you have to look at what happened the seasons after they left [Hiddink won the FA Cup, Di Matteo won the FA Cup and Champions League after coming in mid-season].
"What that does is that sends a message to the club's supporters that change isn't a bad thing. I don't think Sarri is getting that support from his own supporters and that is the big problem. His big problem is who is actually supporting this man if the board aren't.
"We are not speaking about Arsenal and Unai Emery, who are on the same points as Chelsea. Chelsea are in a cup final too. We are speaking about Sarri because it is Chelsea and what they have done in the past. I would like to see them stick with Sarri, but unfortunately we know that these next set of fixtures, because it is Chelsea, will be crucial.
"Top four is everything to these clubs now, even more than the cup final. The Tottenham game will be key to this as opposed to the others. As soon as Chelsea's hierarchy feel they could miss out on the top four, that is when they will feel they can make a change.
"We often see teams at the bottom throw the dice and take a risk, and we might see Chelsea do the same, and see if a new coach will get them into the top four. If Sarri wanted to come into a club and implement his own style of play, which will take time, he may have actually picked the wrong club."