The France international is a doubt for Arsenal's clash with a knee injury, while Per Mertesacker is available after missing Saturday's victory over Sunderland through illness.
The striker, who has netted four goals in his opening four Premier League matches this season, revealed he twisted his ankle against Sunderland on Saturday but insisted he would be fit for his side's match at the Stade Velodrome.
But the Arsenal boss claims the France international's inclusion is now in doubt, with the forward set to be examined on Tuesday.
"We have a few problems. Some with [Mesut] Ozil, but the main one is Giroud, who has a knee problem. He will have a test tomorrow and hopefully he will be fit. But it will only be decided tomorrow," Wenger told the club's official website.
When asked about a potential replacement if Giroud is ruled out, Wenger replied: "I have not really thought about it that much but the obvious solution is [Theo] Walcott. We’ll see."
The Arsenal boss has also confirmed Per Mertesacker is available after missing his side's victory at the Stadium of Light through illness and is optimistic Ozil will also be fit to face Marseille.
"There is good news. Mertesacker will be available again after illness," Wenger said. "[Ozil] was ill and has some tight muscles after Saturday. But I think he will be okay. We are optimistic."