The Reds are long-term admirers of the former Real Madrid and River Plate forward, and with Brendan Rodgers yet to be convinced by summer signing Mario Balotelli, a move for his signature has emerged as a possibility.
Higuain only joined the Naples outfit in 2013, however a £30m release clause has left the door open for a deal.
And Napoli’s move to snap up Manolo Gabbiadini from Sampdoria in an £11m raid appears to have cleared the way for the prolific hit-man to leave.
The southern Italians are also under pressure to balance the books to align with UEFA’s Financial Fair Play rules, which could force them into working out a deal.
Higuain is expected to look for a summer move at the latest, and reports suggest that he could move those plans forward.