Borini has been a key man for the Black Cats since Poyet took charge, despite being signed by former boss Paolo Di Canio.
The Italian failed to settle on Merseyside and was quickly dismissed by boss Brendan Rodgers, however his current form may be enough for the Anfield boss to rethink the strikers’ future.
Poyet is adamant that he wants Borini to stay, however a fee for the player may be out of Sunderland’s league if Liverpool play hard-ball.
“He is going to be important, if we stay in the Premier League I would keep him, as he is very welcome here and the fans like him,” Poyet said.
“Fabio is the perfect character to have in a group of players, professional, he cares, he gives everything – the perfect professional.”
Borini scored in the Capital One Cup final for Sunderland at the start of the month, which was just his sixth goal for the club.