The Reds are set to delve into the transfer market at the turn of the year in a bid to replace Simon Mignolet, who has been criticised for shaky displays throughout 2014.
Although the Belgian only arrived at Anfield around 18 months ago, Brendan Rodgers is thought to have lost patience with him, prompting talk that a new No. 1 will be drafted in before too long.
And Neto is seemingly the man the Kop boss wants, with reports claiming that he has been offered a massive deal to make the move.
The Brazilian stopper is set to be a free agent at the end of the season, and La Viola are aware that selling when the transfer window opens rather than letting his contract run down is a far more intelligent way to go about things, given that the South American is reluctant to commit to the Florence club.
Roma are also after the goalie, but the Serie A giants are unable to compete with the salary of offer on Merseyside, which is likely to sway the 25-year-old.
Neto has been one of Italian football’s top performing ‘keepers in recent seasons, and joined Fiorentina from Atletico Paranaense in 2011.