Jurgen Klopp has been hard at work in the transfer market as he looks to build a side capable of challenging on four fronts.
Alisson, Fabinho, Naby Keita and Xherdan Shaqiri have all been added to the squad which reached the Champions League final last season.
Liverpool want further reinforcements though, with a whole host of players still being linked with moves to Merseyside as a result.
La Gazzetta dello Sport reporter Velluzzi says Liverpool are interested in prising Barella away from Cagliari.
Barella made 34 appearances in Serie A as Cagliari beat the drop at the expense of Crotone last season.
And Velluzzi suggests there could be a battle on for the 21-year-old midfielder this summer.
“[Cagliari] has understood that it may be the right year to sell him,” Velluzzi told RMC Sport.
“He was very professional, even if he has not opened his mouth so far, it means that he wants to understand how the situation will be defined.
“Inter [Milan] currently does not have an urgent need to try to buy Barella, unless they sell [Matias] Vecino.
“There is also Roma at stake, there are also Lyon, Liverpool and perhaps Atletico Madrid.”
While Klopp could bolster Liverpool’s midfield with Barella, the German has ruled out signing another defender.
“This summer? No,” said Klopp, when asked about strengthening at the back. “I’m happy with our players to be honest. I don’t see the need.
“Joe Gomez brings a lot of things that we don’t find on the transfer market to be honest.”
Meanwhile, Liverpool play the penultimate game of their pre-season schedule when they take on Napoli on Saturday.