The Welshman's last contribution for the Gunners was a hat-trick against Everton on February 3, but Ramsey has been out with a groin strain since that match.
Wenger, who has confirmed that the 27-year-old is out for the clash with their Swedish opponents on Thursday, did not rule out Ramsey's participation in the EFL Cup final on Sunday.
"Ramsey is not in the squad for tomorrow," the Frenchman told reporters at a press conference. "He had a good training session but he's not available for tomorrow.
"We will see how his evolution goes between now and Sunday. I don't rule him out. It depends how well he can improve the intensity of training."
Arsenal have a three-goal cushion against Ostersunds from the first leg last week.