0220 GMT August 22, 2019
No deal has been agreed yet but the Italian side wants to bolster its squad before it resumes after its winter break on 8 January, BBC reported.
Lucas, 29, is not Inter's only option but club sources have indicated there is a "strong possibility" of the move going through.
The Brazilian is Liverpool's longest-serving player.
Lucas joined Liverpool from Brazilian side Gremio in 2007 and has been capped 24 times by his country.
He has played 324 games in all competitions for the Anfield side but has started only three games in the Premier League this season.