Sportmediaset and FootballItalia say Napoli will pay €2 million to have the Brazilian midfielder on loan for one season, plus an option to buy for a further €10m in July 2015.
The 27-year-old Brazilian has been a peripheral figure at Anfield since Steven Gerrard’s move into a deeper midfield role at the start of 2014.
When tasked with playing a more advanced role, Lucas has struggled and lacked the dynamism for the role.
Napoli loaned former Liverpool goalkeeper Pepe Reina for the season, then turned down the opportunity to make the move permanent this summer.
Lucas has made 244 appearances for the club since signing from Gremio for £5 million in 2007.