Sky sources understand the 24-year-old Scot has asked to leave the Championship club as the Black Cats continue to try and negotiate a double deal for him and winger Will Buckley.
Poyet has refused to discuss his January targets in public, but the 46-year-old Uruguayan is known to admire a man he took to the Amex Stadium in August 2010.
Whether or not former Chelsea trainee Bridcutt's move will persuade Brighton, who declined to comment on the matter on Tuesday evening, to part with one of their most prized assets remains to be seen.
Poyet has already signed Fiorentina defender Marcos Alonso on loan for the remainder of the season, but hopes to bring in up to four more players before the end of the month.
Sunderland currently sit bottom of the table - four points from safety - with just 14 points from their opening 20 games.