Conte's job is on the line after their humbling by Bournemouth last night.
The London Evening Standard says the club have begun compiling a wish-list of replacements in case the Italian leaves, with Luis Enrique at the top of it.
Despite rumours to the contrary, there did not seem to be a genuine possibility up until now that Conte would depart before the end of the season.
Conte admits Chelsea should be worried about missing out on qualifying for the Champions League.
He said: “We are doing everything and I'm exploiting this squad at the maximum level. But if someone doesn't agree about this, I have to accept the situation. I'm very relaxed about this. I know I'm doing a great job."