Borini, who enjoyed a successful season-long loan at Sunderland last term, is set to move for a fee believed to be around £14million with the decision now resting with the 23-year-old.
The Italy international scored 10 goals for the Wearside club and is reportedly keen to return to the north-east to continue his development under Gus Poyet.
But Liverpool did pick Borini to start Saturday's pre-season friendly against Preston at Deepdale.
Borini, who was Brendan Rodgers’ first signing after joining as Liverpool manager, scored just two goals in 20 appearances during an injury-plagued first year at Anfield.
The former Chelsea youth was signed from Parma in the summer of 2012, having impressed the previous season during a loan stint at Roma, where he scored nine goals in 24 appearances.
Borini made his Italy debut – which remains his only cap to date – in February 2012.