The news comes after reportedly successful talks in London Wednesday between the 73-year-old former Leicester tactician and Chairman Dan Friedkin and his son Ryan.
The deal only has to be officially announced, the sources said.
The Serie A side need a new coach after sacking Ivan Juric on Sunday following a 3-2 home defeat to Bologna that leaves them four points above the relegation zone in 12th place.
The team had hired former Torino coach Juric in September to replace club legend Daniele De Rossi after a winless run in their first four Serie A games of the season.
Ranieri is best known for the football fairy tale of leading Leicester City to the Premier League title in the 2015-16 season.
He was previously in charge of Roma from 2009-2011 and for a short spell in 2019.
He had said he would not coach another club, but was open to taking over a national team, after guiding Cagliari to safety in Serie A last season.
ANSA