The 22-year-old, who has scored 14 times in 25 appearances this season, is widely regarded as one of the best talents in Spain.
A number of European clubs have been linked with his services in recent months, but Arrasate has claimed that the Frenchman is "focused" on his role at Sociedad.
"I see Antoine Griezmann very happy. He's focused on his job and eager to reach his best level. We've spoken every day and he's gotten over his discomfort. I don't think anyone will leave this window, but this is football and nobody knows what will happen," Arrasate told reporters.