The London Evening Standard says Spurs have had a £15million bid for the 23-year-old rejected by Real Sociedad but are looking to return with a higher offer.
Griezmann is keen to leave the La Liga side and has already rejected terms on a contract extension.
He has a £25m release clause in his current contract, which chairman Daniel Levy might be reluctant to meet after the £56m signings of Erik Lamela and Roberto Soldado fail to come off last term.
Griezmann is believed to be close friends with France keeper Hugo Lloris, who has just signed a new five-year contract at Spurs after being reassured by Levy that significant new signings will be made.
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