The Italian spent the last campaign on loan at Sunderland, where he scored 10 goals in 40 games.
"Fabio goes back to Liverpool to stay there, as stated by the manager Rodgers a few weeks ago," he told Calcionews24. "So far, Liverpool have not received any communication regarding his transfer.
"I would not be surprised if there were other clubs who want him because I consider him a complete striker, but for the moment, all I can say with certainty is that Fabio has returned to Liverpool to stay."
Borini joined Liverpool from Roma in 2012 for a reported fee of £10m.