The 21-year-old defender came through the youth system at the Sussex club, and has made 44 league appearances for the Seagulls.
In September 2011 it was reported that Arsenal were keeping tabs on Dunk, and he played 36 league games last season.
However, he has struggled to gain a first-team place this season, making just seven appearances in the Championship. He was sent off after just eight minutes of Brighton's game against rivals Crystal Palace last month.
It now appears that Brighton may be prepared to listen to offers for Dunk, and Championship rivals Bristol City and Blackburn are thought to have shown interest in the signing.
Given that Dunk's current contract expires at the end of the season, it is thought that the player would not command a sizeable fee.
Dunk was called up to the England under-21 squad in November 2011.