Press Association Sport understands the 24-year-old Scot has asked to leave the Sky Bet Championship club with the Black Cats having been engaged in advanced talks for both he and winger Will Buckley for several days.
The Barclays Premier League outfit has as yet been unable to broker deals for the pair with Bridcutt in particular a man Poyet covets as he looks to bolster the squad he inherited from predecessor Paolo Di Canio.
He 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, but Poyet will be keeping his fingers crossed.
He 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.
The Black Cats, who face Manchester United in the first leg of their Capital One Cup semi-final at the Stadium of Light on Tuesday evening, currently lie bottom of the table with just 14 points from their opening 20 games.
They remain just four points adrift of safety, but are well aware of the fact that only West Brom in Premier League history have gone into Christmas in last place and avoided the drop.
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