The French international is on the radars of the Reds and the Blues on the back of his excellent displays in La Liga last term and at the World Cup in recent weeks.
With a release clause of £24m in his contract at the Anoeta, Sociedad are aware that they may well be unable to keep their man – particularly after he turned down a fresh deal last week.
While Chelsea and Liverpool are being mooted as favourites to snap him up, Spurs are also in the hunt.
New Lilywhites chief Mauricio Pochettino is expected to spend in the coming months, and Griezmann is a top target of his.
The presence of Hugo Lloris may be a positive factor for them, with the goalkeeper Les Bleus’ captain and an influential figure.
Meanwhile, Tottenham are also closing in on Swansea left-back Ben Davies after agreeing a £10m fee for the Welshman.