Barnes is entering the final year of his contract at the Amex Stadium and the 23-year-old has yet to be offered a new deal.
The news has alerted a host of Barnes' suitors with the former Plymouth man establishing himself as one of the best strikers in the Championship.
Barnes finished as Brighton's top scorer in their first season back in the Championship in the 2011-12 season with 14 goals and he scored nine goals last term despite missing seven games through suspension.
Norwich and Hull are both thought to be admirers of Barnes and are actively monitoring his situation on the South coast.
Brighton would be loathe to lose Barnes, but they are bracing themselves for bids for the skilful attacker.