The forward has entered the final year of his contract at the Amex Stadium, and has been subject to reported interest from both Norwich and Hull.
It now seems that Brighton will do all they can to keep the striker, offering a new deal.
Barnes has scored 41 league goals since arriving at Brighton from Plymouth Argyle in 2010, and in 2011/12 he was the club's top scorer with 14 goals in all competitions.
The 23-year-old was the subject of controversy last season when he shown a red card for trying to trip up a referee during the latter stages of a match against Bolton. Barnes was given a seven-match suspension for the incident.