As the report also indicates, Suarez has clashed with manager Paulo Sousa and struggled to settle with the Florentine side having made just four Serie A appearances since joining, the last of which came in September.
In the four league matches since, the defensive midfielder has been an unused substitute.
The 28-year-old was part of the Atletico Madrid side that won La Liga in 2013-14 and reached the Champions League final in the same season, but the Spaniard isn't the player who can elevate Liverpool's midfield.
According to Squawka, Suarez attempted 56 tackles in 20 La Liga appearances last season, but won just 19—an uninspiring success rate of just 34 per cent.
Indeed, compared with Liverpool's own defensive midfielder Lucas Leiva, who made the same number of appearances in the Premier League last year, Suarez firmly comes off second best.
On average per game, Spaniard had a lower pass completion rate than the Brazilian and made comfortably fewer tackles, interceptions, blocks and clearances according to Squawka.
If Liverpool are hoping to bring in a midfield enforcer to replace Lucas, Suarez isn't the candidate to do so.
Gazzetta dello Sport (h/t the Mirror) also report that another player unlikely to be arriving at Anfield from Serie A is Atalanta goalkeeper Marco Sportiello. Liverpool are "said to be contemplating a move in January" for the stopper, but Sportiello insists he's happy where he is for the time being:
Last summer one day they had me joining Ajax, another day Stoke City, then Stuttgart and Roma and even Liverpool. But I was always certain I would stay, it was right thing to do since I need to confirm what I did last season.
I feel at home in Bergamo. I've worn this jersey for seven years and arriving in Serie A was fantastic. We'll see what happens in the future.
BeIN Sports commentator Matteo Bonetti believed the 23-year-old to be the stand out keeper in Italy last season:
According to ESPN's Dale Johnson, only Freiburg's Roman Burki made more saves in Europe's top five leagues last season than the Italian's 138. WhoScored.com share a similar stat for Reds 'keeper Simon Mignolet:
However, Atalanta are a typically struggling team in Serie A and finished 17th last season—just three points ahead of relegated Cagliari in 18th. Likewise, Liverpool's defence has been found wanting for quite some time, so both 'keepers will have been among the more active in their leagues.
Mignolet does boast another impressive stat though:
The Belgian has endured some difficult times in his Liverpool career and made some high-profile errors, but the 27-year-old is currently performing fairly solidly, so a replacement isn't likely to be high on Liverpool's list of transfer priorities.
Sportiello is a promising 'keeper and could make valuable competition for Mignolet, but it doesn't look like he'll be departing Italy in the immediate future.