Borini, who cost Liverpool more than £10million when they signed him from Roma in 2012, spent last season on-loan at Sunderland, and he was a big hit on Wearside.
Sunderland boss Gus Poyet has not hidden his desire to bring the 23-year-old back to the Stadium of Light - but his future is in the hands of Liverpool boss Brendan Rodgers.
Rodgers has stated that he is ready to welcome back Borini this summer, meaning Sunderland will have to wait and see if he figures in their plans for next season.
But Borini's agent feels he will be staying at Anfield.
"Fabio goes back to Liverpool to stay there, as stated by the manager Rodgers a few weeks ago," Marco De Marchi 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."