'The Express' reported on Monday that Antonio Conte only has 48 hours left at Stamford Bridge, although they suggested his replacement would be Luis Enrique.
However, Chelsea could move in a different direction given the comments made by Laurentiis.
When asked about how negotiations with Sarri were progressing, he said: "There is no more time for [him], he didn't answer. Ask him.
"He has always just sent me to Allessandro Pellegrini (Sarri's agent), he never gave me an answer, he only replied: 'boh'!
"I have to take responsibility. At some point we have to move forward. I'm not saying he will leave. There is a release clause, we'll see what will happen".
Sarri's contract doesn't expire till 2020 and includes a release clause of £7million, which could be cheaper than if Chelsea were to move for former Barcelona boss Luis Enrique.