Manager Arsene Wenger told reporters on Tuesday the Premier League leaders had yet to receive a specialist's report on Ozil's shoulder injury and that Ramsey would be out for three more weeks with a thigh strain.
The pair both missed the 1-0 league win at Newcastle United on Sunday.
Giroud, who scored the only goal at Newcastle, will miss out against Cardiff because of an ankle injury and left back Gibbs has a calf problem.
Wenger also said he was uncertain about the fitness of defenders Nacho Monreal and Thomas Vermaelen, midfielders Tomas Rosicky and Jack Wilshere and striker Theo Walcott.
Arsenal go into the match with a one-point lead over Manchester City and Wenger said he was proud of the fact his side accumulated more points in 2013 than any other team in the league.
"It's not a trophy but it shows the consistency and the trend for the team," he said. "If you can manage from January 1 to December 31 to have that trend it means we are going upwards.
"We want to transfer that trend into 2014 and to have a great race for the Premier League title. In 2013 we have been relatively consistent and that makes the belief stronger."
Wenger, who will look to end a nine-year trophy drought in 2014, said he was thoroughly enjoying being around his current squad.
"This team has a remarkable attitude and as a manager for me it is a privilege to manage them as a group of players on the pitch but also off the pitch because they have a classy attitude," the Frenchman added.
(Writing by Tony Jimenez; editing by Ed Osmond)
