Despite finishing third in the Premier League and guiding the club to the Europa League final, there are still some doubts surrounding the manager’s future.
The Italian has struggled to win over the supporters with Sarri-ball, with his players struggling to get to grips with the possession-based style of football he brought to west London from Naples.
According to Sport Mediaset, Sarri will ask the Chelsea board for time to consider his future at the end of the season.
For now, he is fully focused on the Europa League final against Arsenal in Baku, where he will look to win his first ever trophy as a manager.
Having previously claimed he wants to stay in the Premier League, Sarri is also enticed about a potential return to Italy.
Roma are one club who are interested in appointing the Tuscan coach, while there have been rumours linking him with Juventus and AC Milan, who could part ways with their current bosses when the season finishes.
Chelsea also have a plan in place if Sarri is to turn his back on the club.
Lampard is being eyed as his potential successor according to the report.
The former midfielder has made an impressive start to management with Derby, having led them to the Championship play-offs.
Lampard said in May last year that he would struggle to turn down the opportunity of a return to Stamford Bridge should the opportunity come knocking.
“Chelsea, of course, is like a dream job that will be there one day. But that is not always the route that it takes, so it might take me to go somewhere else before I can ever do that,” he told Goal.
“We will see, but I certainly have ambitions to do it.
“How could I not take it if Chelsea offered me the job?
“Chelsea are my club and I feel like I have a lot to offer. But that’s obviously for other people to decide, for important people, if and when I am ready to do that.”
Chelsea and Arsenal go head-to-head on Wednesday 29 May in Azerbaijan in the Europa League final.