Sunderland, who are managed by former Brighton boss Gus Poyet, sit bottom of the Premier League table and are looking to bolster their squad in the January transfer window.
They have been regularly linked with a move for the 24-year-old Bridcutt, who has played at Brighton since joining on a free transfer from Chelsea in July 2010.
And the Championship club confirmed Sunderland's interest in the midfielder on Wednesday, releasing a short statement that said they had turned down the midfielder's plea to leave.
"Further to reports in today's media, 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," it read.
"At this stage the club does not wish to make any further comment on this matter."
Brighton sacked Poyet for gross misconduct in June, but was hired by Sunderland in October in place of the axed Paolo Di Canio.
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