The France attacker is off contract in June and has baulked at Barca's attempts to open talks about a new deal.
Manchester United are keen, as are Newcastle United's new owners, which are regarded as favourites for Dembele's signature. Both Premier League clubs are offering major signing bonuses to Dembele to tempt him to England.
Mundo Deportivo says Spurs are also keen, with football chief Fabio Paratici driving the move.
Paratici also tried to sign Dembele for Juventus and has maintained his admiration for the player.
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