The 67-year-old - who famously led Leicester to an unlikely English Premier League title in 2016 - has reportedly said the chance to manage the Hoops is a “temptation” for him.
Calciomercato also claims the former Nantes and Monaco boss is on Celtic’s radar as they look for a permanent successor to Brendan Rodgers.
Ranieri, dubbed “Tinkerman”, had an unhappy spell in charge of Fulham this year, and is currently at Roma - but the former Chelsea boss is set to leave the Italian capital in the summer.
Slaven Bilic - linked with the Scotland job earlier this year - emerged as a contender for the Celtic role earlier this week. The former Croatia boss is keen to get back into management since leaving Saudi Arabian side Al-Ittihad.
The 50-year-old was understood to be keen on the Scotland job but is believed to favour a club role over an international job, and the former West Ham manager is interested in the Celtic job according to reports.
Former France and Paris Saint-Germain manager Lauren Blanc has also been linked with the Celtic role as speculation rumbles on.