The 21-year-old has caught the eye of top clubs across Europe thanks to his fine form for the Scottish Premiership side over the last 18 months, his contribution of 40 goals in all competitions helping them to a remarkable unbeaten domestic run of 67 games.
Manchester United, Arsenal, Chelsea, Everton and Marseille were all linked with the former Fulham forward over the summer but a bidding war failed to materialise after Celtic gave him a price tag of £30m.
According to the Daily Mail, the Seagulls are now contemplating testing the Bhoys' resolve when the transfer window opens and will make an opening offer of £20m for Dembele - a figure that eclipses the club-record £13.5m paid for Jose Izquierdo in August.
Chris Hughton's side, who sit 12th in the Premier League, are in the market for firepower this winter, having failed to land a number of strike targets - including Vincent Janssen from Tottenham Hotspur - over the summer.
Dembele has two-and-a-half years remaining on the four-year deal he signed when he joined Celtic for just £400,000 last year.