With both sides struggling at the foot of Group F, each six points adrift of Bayern Munich and Olympiakos Piraeus, their chances will be buried unless one of them can win at the Emirates Stadium on Tuesday.
Even then, they have to rely on the prospect that Bayern and Olympiakos do not play out a draw at the Allianz Arena.
Yet Wenger's hopes will have been raised by a period of turmoil for Zagreb, who were hit by two scandals in a space of three days last week.
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Their chief executive Zdravko Mamic was arrested on Wednesday for alleged transfer irregularities, while midfielder Arijan Ademi was handed a four-year doping ban on Friday after testing positive following Dinamo's 2-1 home win over Arsenal in September.
Wenger is remaining optimistic that his side, whose faltering form continued with a 2-1 defeat at West Bromwich Albion on Saturday, can still overcome long odds and continue their remarkable record of consistently reaching the last 16.
"If you ask my deep gut feeling, I want to stay in the Champions League," the Frenchman told reporters when asked if failing to make the last 16 might actually aid their Premier League title ambitions.
"We will give absolutely everything to stay in the Champions League.
"I think we still have a strong chance but it will be very tight now."
After watching his side hammered 5-1 at Bayern Munich in their last European outing, Wenger said: "Let's hope Bayern beat Olympiakos and we win at home against Zagreb, which would leave us with a chance to qualify from the last game."
Zagreb's victory over Arsenal in the first round of matches was shrouded in controversy with Ademi's failed drugs test. Wenger then repeated his calls for stronger anti-doping measures from football's authorities.
Yet Ademi claimed he was innocent while his coach Zoran Mamic told the club's website (www.gnkdinamo.hr): "To punish a player for four years after he and the experts proved that he took a contaminated supplement is senseless."
Dinamo at least eased some of their off-pitch woes with Friday's 2-1 win at Slaven Belupo Koprivnica, which kept them second in the first division, two points behind leaders Rijeka.
(Additional reporting by Zoran Milosavljevic; editing by Toby Davis)
