An injury soon after moving to Anfield pushed the striker down the pecking order, while first-team chances have not been forthcoming while on loan at Sunderland
The striker has seen his opportunities limited since moving to the Premier League from Roma in 2012 and has concerns over whether he will be able to force his way into Italy's 2014 World Cup squad.
Despite agreeing to join Sunderland until the end of the season, Borini's representative believes the player will be looking elsewhere in the new year.
"Liverpool own him and in the summer didn't want him to leave, even though the player wants minutes," Marco De Marchi is quoted as saying by the Daily Mirror.
"He dreams of Brazil in 2014 and needs games. He's only had a chance at Sunderland after the arrival of Gus Poyet, but it is still insufficient.
"I would like a meeting with Liverpool in January."
Borini has made seven league appearances for Sunderland so far this season, with his only goal being the memorable winner in the derby encounter with Newcastle United on October 27.