Wenger took close to a full-strength squad to Sweden for the first leg which his side won 3-0 last week and will look to give his younger players some game time on Friday (AEDT).
Ozil and Ramsey were involved in first team training on Thursday (AEDT) but Wenger said the Germany playmaker had struggled with illness this week while the Wales international needs more time prove his fitness after returning from a groin injury.
"He (Ozil) was in bed Monday, Tuesday for sickness," Wenger told a news conference. "I would certainly have played him, but because he was sick he will have to work hard tomorrow and will not be involved.
"Ramsey's not in the squad tomorrow, he had a good training session. We will see how his evolution goes between now and (the League Cup final on) Sunday (Monday, AEDT). I don't rule him out."
Wenger confirmed Henrikh Mkhitaryan will be given the responsibility of producing chances going forward in the absence of Ozil, and Danny Welbeck will start up front.
Goalkeeper David Ospina, who has been picked for the majority of Arsenal's matches in cup competitions this season, will keep his place ahead of first-choice Petr Cech.
Arsenal are sixth in the Premier League, eight points adrift of fourth-placed Chelsea, and need to finish the season in top-four or win the Europa League to qualify for next season's UEFA Champions League.
When Wenger was asked whether he would prioritise the Europa League as Manchester United boss Jose Mourinho did last term, the Frenchman replied: "He did that much later, once they were in the semi-finals.
"We have to focus on the Premier League. It (Europa League) is one of the priorities we have. We are focused to do well. But ideally we want to come back to the Champions League through the Premier League."