The Italian spent last season on loan at the Stadium of Light and impressed as the Black Cats avoided relegation and came close to lifting the Capital One Cup.
However, he has since returned to Merseyside, since which time his agent, Marco De Marchi, has talked up the 23-year-old’s prospects at Anfield.
But with Loic Remy now edging towards a switch to Liverpool, Brendan Rodgers is thought to have deemed his first signing at the club in 2012 as surplus to requirements.
Yet Borini is not yet ready to leave, and is thought to have been taken aback with the speed at which his move is going.
It is understood that Sunderland have not been in contact with the one-time Italian international.
Borini may well eventually opt to leave, with Remy’s imminent arrival likely to push him further down the attacking pecking order at Liverpool following the signings of Rickie Lambert, Adam Lallana and Lazar Markovic.