Midfielders Tomas Rosicky (calf) and Jack Wilshere (ankle) both face fitness tests later on Tuesday, as does England forward Theo Walcott, who picked up a shoulder problem in the 1-0 win at Newcastle.
Full-back Kieran Gibbs definitely misses out because of a calf strain, while fellow defenders Nacho Monreal and Thomas Vermaelen have both been laid low by illness.
Midfielder Aaron Ramsey is expected to be unavailable for around three weeks with the thigh problem suffered in the win at West Ham on Boxing Day, while German playmaker Mesut Ozil is also sidelined, with the club awaiting results of a visit to a shoulder specialist.
"You need a good memory because we have plenty of problems," said Wenger, whose side head into 2014 top of the table by a point from Manchester City.
"Ramsey and Ozil are out. Ramsey (for) three weeks and Ozil has seen a specialist last night, I haven't got a report yet.
"We lost Gibbs at Newcastle with a calf strain. We have as well Monreal and Vermaelen, who are not sure to be ready because they come just back from illness, then we have uncertainty about Rosicky, Wilshere and Walcott.
"We lost Giroud on an ankle problem at Newcastle, so this morning will be more a medical check to see who will be available for tomorrow's game."
Wenger, though, moved to allay any worries Giroud's injury could be a long-term concern.
"Olivier is a strong structure and he recovers quite quickly," said Wenger of the France striker, whose second-half header secured victory at Newcastle to end his mini-goal drought.
"He thinks he will be all right for Saturday, but the medical people think he will be a bit short. He is quite optimistic about it."
Wenger must decide whether to start Lukas Podolski, who scored on his return from a four-month injury lay-off at Upton Park, or Nicklas Bendtner in attack against the Bluebirds.
"I have to see how I can balance the team because I have to consider as well who else is out and how can I get a balanced team out there," he said.
Wenger will measure up Arsenal's options ahead of the transfer window opening again on New Year's Day.
"We are like many clubs, we are certainly on alert if something special turns up we will not turn it down, but we are not as well desperate because we have a big depth in our squad," the Arsenal boss said.
"We have shown that because our midfield for example at West Ham and at Newcastle was completely different - we changed three players and we still managed to have a very strong team."
France international Giroud admits he would "rather not see a new striker come in" next month.
Wenger, though, maintains Arsenal are not looking to replace their 11-goal forward, rather offer him support.
"Would you expect anything different from a striker?" said Wenger when asked what he thought of Giroud's comments to French TV.
"I believe we have to give him credit for one thing, that physically he has coped with it until now in a remarkable way and with a fantastic combative attitude.
"I don't know if we will do something or not (in January), but it is not to replace Olivier Giroud - we have a great confidence in Olivier Giroud."