The newspaper claim on their website that Lazio have agreed to pay the Merseyside giants £5million for the 30-year-old Brazilian.
The Mail report that Lucas is in negotiations with the Serie A big hitters over personal terms as they aim to seal his signature at the start of next week.
This comes after Times correspondent Paul Joyce claimed on his personal Twitter account yesterday that Lazio had tabled a £5million bid for Lucas and that he would not be in the Liverpool squad that hammered Tranmere 4-0 in a friendly on Friday night.
Lucas is now in line to end his 10-year spell at Liverpool after joining from Brazilian side Gremio in 2007.
The midfield anchorman made 31 appearances across all competitions last season, but just 12 of those were Premier League starts and he now appears to have played the last of his 346 appearances for the club.
Lazio are currently managed by Simone Inzaghi and will compete in the Europa League next season after a fifth placed finish in Serie A.