Sarri was replaced by Carlo Ancelotti at Napoli amid growing links with Chelsea, where fellow Italian Antonio Conte is tipped to leave.
The 59-year-old Sarri – who Goal understands is nearing a move to take over the Blues – guided Napoli to their second runners-up finish in three seasons, having threatened to dethrone Serie A champions Juventus this term.
Ranieri – a Premier League-winning manager with Leicester City – spent four years at Chelsea before he was sacked in 2004 and he warned Sarri about owner Roman Abramovich.
"He'll have to work hard, and that's not something he lacks.
"Sarri has done well at every level, including Empoli where people said he wasn't ready for big teams.
"Now they know him all over Europe and I'm sure he can take his football and his philosophy anywhere."
Ancelotti is reportedly set to be backed heavily in the transfer market by Napoli president Aurelio De Laurentiis and Ranieri said: "I was a bit surprised, I imagined Carlo abroad.
"I have to congratulate De Laurentiis who has pulled off a big coup, because he's brought the most decorated Italian coach, who has won so much abroad, to Napoli."