Despite winning the Premier League title in record breaking fashion last season and following it up with FA Cup glory over the weekend, Conte is rumoured to be close to the sack and fellow countryman Sarri has been installed as the favourite to take over.
That has left De Laurentiis with little choice but to give up as the 59-year-old looks set for the door. Napoli will, however, ensure they are not short changed if Sarri is to move on.
"There is no more time for Sarri, he didn't answer," De Laurentiis is quoted as saying by the Daily Mirror following the end of the 2017/18 Italian season at the weekend.
"Ask him, he has always sent me to Pellegrini (Sarri's agent), he never gave me an answer. I have to take responsibility. At some point we have to move forward. I'm not saying he'll leave. There is a release clause, we'll see what will happen."
Former Barcelona coach Luis Enrique and ex-Chelsea boss Carlo Ancelotti are the other names currently most favoured by bookmakers to become next permanent Chelsea manager, but Sarri would appear to be the best bet at this moment in time.