Italian outlet La Nuova Sardegna is reporting that the Reds have added the 21-year-old to their transfer wish-list ahead of the summer window.
The same report also credits Bundesliga side Borussia Dortmund with a strong interest in signing the attacking midfielder this summer.
The story says that Cagliari are prepared to consider offers of between €40m and €50m to sell Barella this summer and that Juventus are among the other clubs keen on the midfielder.
Barella has been in good form for the Sardinian side this season, scoring five goals and making one assist in 26 Serie A appearances for the Italian club. He has also made one appearance in the Coppa Italia.
Liverpool FC are likely to be on the lookout for reinforcements this summer as Jurgen Klopp looks to assemble a squad capable of challenging for the title next season.
The Reds are currently preparing for their crunch clash against Manchester City on Wednesday night in the first leg of their Champions League semi-final tie.
Liverpool FC are in third place in the table as they seek to book their place directly in the group stage of next season’s Champions League.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news