AC Milan are the latest European heavyweights to be credited with an interest in the player. The Italian giants are in talks to sign the French Under-21 international, according to Sky Sports.
Dembele, 20, scored 32 goals in all competitions for Celtic last season, 17 of them coming in the league. It was a remarkable return in his first campaign since joining the club last summer from Fulham for just £500,000. Celtic were invincible domestically, claiming the treble of league, Scottish Cup and League Cup without losing a match.
Celtic claim they have no desire or need to sell the player but a bid in excess of £30 million would test their resolve.
With so much interest in the player, a bidding war could develop over the summer, with AC Milan likely to face competition from Borussia Dortmund, Sevilla, Chelsea and Olympique Marseille.
Celtic, meanwhile, are expected to step up their bid to sign Jonny Hayes from Aberdeen. Manager Brendan Rodgers knows the player from their time together at Reading. The winger has two years remaining on his Pittodrie contract and it would take a substantial bid to persuade Aberdeen to sell the 29-year-old.