Contrary to reports linking him with West Ham, Gazzetta dello Sport claim the striker could be on his way back to Rome.
The report contradicts suggestions by The Sun that the attacker is ready to switch to West Ham and that a medical is in the offing.
The former Sunderland loanee has seemingly slipped down Brendan Rodgers’ pecking order further following the impending arrivals of Roberto Firmino and Danny Ings this summer.
Gazzetta state that Lazio are leading the chase for Borini, but face competition from Fiorentina.
The story also claims that the Reds are willing to accept a fee in the region of €7 million (£5m) for Borini and are planning for life without the versatile forward next season.
Both Borini and compatriot Mario Balotelli have come in for criticism over the last 12 months as they have failed to fire Liverpool towards the top four.
With the Merseysiders missing out on Champions League football ahead of next season, Rodgers looks to be keen to revamp his squad ahead of 2015-16.