The French midfielder was rumoured to be a top target for the Gunners during the January transfer window.
No move was made, though, and the 22-year-old remains in Spain.
There may, however, be an approach being readied at Emirates Stadium, with thoughts already starting to turn towards the summer market.
Wenger likes to keep his transfer cards close to his chest and has refused to be drawn on whether a bid will be tabled.
But the Gunners boss has admitted to being among those closely monitoring Griezmann's situation.
He told French football television show Telefoot: "Yes, we follow him in great detail.
"He attracts other clubs as well. But we follow him, he is a known commodity."