The 29-year-old, whose former clubs include Chelsea, AC Milan and Sunderland, is a free agent having left Serie A side Hellas Verona this summer.
Borini claims he rejected several offers from other Italian sides for his services during the transfer window, as he was holding out for a move back to England.
The former Italy international, who has just the single cap for his country, has been training alone in a park in Liverpool after being told he couldn’t train with his former club or their cross-city rivals Everton.
Now reports claim that Burnley are considering a move to bring in Borini, despite the Clarets being reasonably well stocked in that area.
Burnley fans have been majorly disappointed with the lack of transfer activity at Turf Moor in recent times, with Sean Dyche afforded a paltry £1m to spend on Brighton’s Dale Stephens this summer.
The Clarets’ interest in Borini has been touted by Italian press, who say that Swansea and Watford are also in for the player.
If Sean Dyche does swoop for the Italian he would likely deploy him in a wide area – but it feels like any bodies through the door would do for the Burnley gaffer right now.