Reds boss Brendan Rodgers is desperate to sign central reinforcements this month in a bid to keep his side in the title race after a lack of depth in his squad was exposed over the Christmas period.
Liverpool currently have very little in the way of back up to the likes of Steven Gerrard, Lucas and Jordan Henderson, which is believed to be a major source of concern.
Inler has emerged as the latest name on an extensive list of possible buys, with the Swiss star having been impressive in Serie A for some time.
Although the rugged enforcer may not be available this month, Rodgers is still keen and could launch an end of season swoop.
Napoli are managed by former Anfield chief Rafael Benitez, who is unlikely to be open to doing his old side any favours with Inler a key member of his squad.
However, if the player pushes for a move the Italians may be unable to prevent him joining the Merseysiders.
The 29-year-old is vastly experienced, having represented his nation on 67 occasions. He is also set to play a key role for them at the coming World Cup.