Sky Sports reported on Tuesday that Bridcutt had asked to leave the Championship club following an enquiry from Wearside, where former Albion boss Gus Poyet is in charge.
And Brighton have now confirmed the Scotland midfielder wants out.
A club statement read: "Further to media reports Brighton and Hove Albion can confirm that a transfer request from Liam Bridcutt was received yesterday afternoon and subsequently has been rejected by the club.
"At this stage the club does not wish to make any further comment on this matter."
Poyet has not named his January targets, but Sky sources understand he is interested in both Bridcutt and Brighton team-mate Will Buckley.
Sunderland have already signed Marcos Alonso on loan for the remainder of the season, and Poyet hopes to bring in up to four more players before the end of the month.
Poyet's side currently sit bottom of the table - four points from safety - with 14 points from 20 games.
Meanwhile, Brighton have signed have signed Tottenham striker Jonathan Obika on a three-month loan deal.