The forward, who is currently on loan at Sunderland, is said to be seeking a meeting with the Reds to secure a move away from the Premier League.
"Liverpool own him and in the summer didn't want him to leave, even though the player wants minutes. He dreams of Brazil in 2014 and needs games," The Mirror quotes Borini's agent Marco de Marchi as saying.
"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 joined Liverpool from Roma in the summer of 2012, but his time with the Reds has been marred by injuries.