The former Brazil global has spent over a decade at Anfield but is expected to seal an emotional exit amid an increased level of competition in his role.
But when interest waned, it was thought the 30-year-old would stay on Merseyside, with another year left to run on his current contract.More news: After 4 young Pennsylvania men disappear, DA suspects foul play
And many Liverpool fans are devastated at seeing the Kop man leave the club this summer.
A medical and personal terms are still to be passed and finalised before Lucas can complete the move.
Lazio, managed by Simone Inzaghi, have made an approach to Liverpool and Lucas is considering his options before the squad fly to Hong Kong on Sunday to take part in the Premier League Asia Trophy.More news: Florida county issues 'no homework' policy for elementary schools
Lucas is now Liverpool's longest-serving player, having made 344 appearances for the Reds since moving to Anfield from Brazilian outfit Gremio in 2007.
Talks are ongoing between the relevant parties and could see the player omitted from plans to feature in Friday's friendly against Wigan Athletic.
But with the midfield-trio of Jordan Henderson, Georginio Wijnaldum and Adam Lallana now regular starters for Klopp, Lucas often found himself deployed as a center-back last season.More news: Roku to File for IPO This Year
- Ex-congressional staffers indicted for posting House member's nude video
- Reliance Jio 4G phone photos leaked, reveals its design and features
- U.S. denies visas to Russian replacements for expelled diplomats - Moscow
- Ex-Soviet Military Officer Joined Trump Jr.'s Meeting With Russian Lawyer
- Garbine Muguruza vs Magdalena Rybarikova: Wimbledon 2017 semi-final preview and prediction
- 6 reported killed in crash on I-65 North in Kentucky
- Nawaz Sharif dismisses graft report; terms it as slander
- Body of missing Pennsylvania man found near other human remains, suspect confesses
- Turkish police detain producer of Erdogan film over Gulen links
- Wimbledon: Sania Mirza crashes out, Bopanna advances to mixed doubles quarters