Yesterday's loss 6-0 thrashing at the hands of Man City leaves the club in sixth position.
And Harris believes Sarri will be fired if he can't motivate his side to respond over the next four weeks.
When asked what the future holds for Sarri, Blues legend Harris told Love Sport Radio: "That's for the powers that be [but if I were in charge] I would most probably have a chat with him and say 'you've got until the end of the month to put things right and if not, you're obviously in a precarious position'.
"The knives are out for the fella at the moment but it's up to him now to get the players to rally round.
"Whether he can do that remains to be seen because they're playing Manchester United in the cup, the League Cup final coming up and four or five games in the next couple of weeks so I think he needs to put it right otherwise he will be walking."