A number of top flight Premier League clubs are understood to be keeping a close eye on the French winger including Chelsea, Arsenal and Manchester United.
Griezmann has been in blistering form for the La Liga side and bagged a Monday night hat-trick against Elche to take his tally to 15 this term.
The 22-year-old, who has been at the Basque club for over nine years, says he is likely to discuss his future with the club in the summer.
"I am happy at Real Sociedad, I'm very relaxed about the situation," Griezmann told reporters. "I want to finish the year here, and then we'll see.
"The team is working well and it's important we try and get back into European competition next season."