Borini, who spent the 2013-14 season on loan at Sunderland, started only five games for Liverpool last season and is unlikely to find opportunities any easier to come by after Ings was confirmed as the club’s second signing of the summer.
Borini’s agent Marco de Marchi said: “Soon we will have to talk to Liverpool.
“Several teams have asked for Fabio on loan but the Liverpool board have always refused, especially in light of the £10million bid that was rejected last year from Sunderland.”
Borini became Brendan Rodgers’ first signing as Liverpool manager when he joined for 10.5million from Roma in 2012, and the Reds are only interested in selling rather than loaning out the 24-year-old, according to the Liverpool Echo.
Ings, meanwhile, could cost Liverpool as much as £8million if Burnley get their way, with the Clarets looking for a record tribunal fee in excess of the £6.5million Chelsea paid to sign Daniel Sturridge from Manchester City in 2010.
Liverpool had hoped to agree a fee of around half that, but Tottenham’s bid for the striker, reported to be £12million, convinced the recently-relegated side they can hold out for more.