If they end up replacing Pouchettino so early he'll be the fourth coach third coach they've replaced since Todd Boehly took over ownership from the Rússian business man Abrahamovic,and i think they should be patient enough and believe in Pouchettino to get the team back tova better performance because it would be too early for fans to be calling for his sack, i think the grace of two season would be enough for Pouchettino to take Chelsea back to winning ways just like Arsenal did with Arteta when he came into their club, now he's made the team very strong and very tough to play against.
Pouchettino is an experienced coach and has got an experience in the league before now, about his players, they might notcbe in their best form currently cause some are very young in age and lack the experience but with time they'll begin to pick up because they're talented in as much as they don't got much experience all they need is time to get better.
I don't think that Todd Boehly will replace Pochettino immediately, because this coach has already spent a lot in the transfer market, and changing coaches will not guarantee that there will be changes, we can see when Graham Potter was at Chelsea, Boehly was patient enough to wait for the coach to bring him in. Chelsea is heading in a better direction, only to fail.
Many predict that Chelsea's current situation is because many of their players are injured, maybe that is true but it also proves that Pochettino is not a coach with a lot of strategy, he relies on his strategy on players who are considered capable of doing it and when it doesn't work he doesn't change anything other than waiting until it can work as it wishes.
I predict changes will be made in the middle of the season when nothing good happens to Chelsea, indeed it looks too late because in the middle of the season if their position has not improved it will be difficult to end up in the European zone, but we don't know for sure what will happen in a few months, maybe something good will finally happen to Chelsea, because I don't believe that Chelsea will stay like this without any improvement at all.