The Spanish giants are still looking to strengthen their attacking line after allowing Neymar to leave for PSG and missing out on Philippe Coutinho this summer.
They are keen to avoid a repeat of the sluggish transfer market and according to the mentioned Spanish publication, club chiefs have already identified their man.
Griezmann was linked with a move to a host of European giants this summer, including Manchester United, but Atletico Madrid refused to let their star player leave due to their transfer ban.
As a result, the Frenchman stayed in the Spanish capital out of loyalty and put pen to paper on a new contract with the club.
However, in that new deal, Griezmann has a release clause that is set to reduce to €100m from July 1 2018, a modest figure when compared to the £198 transfer fee paid for Neymar.
The 26-year-old has scored two La Liga goals this season and is currently on international duty with France, who need to win their final World Cup qualifier if they are to book their place at football's showpiece event next summer.