The 24-year-old Italian striker was deemed surplus to requirements at Anfield, with Liverpool having signed Christian Benteke and Danny Ings in the summer.
Borini also attracted interest from several Italian clubs in the summer, but it seems he is ready to join the Black Cats, where he spent a fantastic loan spell during the 2013-14 season.
He scored seven goals in 32 appearances during that loan spell and helped the club escape from the threat of relegation.
Borini, who was Brendan Rodgers’s first signing as a Liverpool manager, has made only 18 appearances last season, mostly as a sub, and has failed to force his way into Brendan Rodgers’s plans at Anfield.
Meanwhile, according to reports from The Telegraph, Liverpool left-back Jose Enrique is also likely to leave the club before the deadline day. West Bromwich Albion are thought to be reportedly interested in signing him.