The attacking duo were forced to sit out part of Die Mannschaft's training session on Wednesday, with Gotze nursing a muscle problem and Podolski recovering from an ankle knock, but Flick has played down any fears that they may be sidelined for the World Cup qualifier in Dublin.
"Today was the first day that every player was there," he told reporters at a press conference.
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Joachim Low's side are already without injured defender Mats Hummels and midfielders Ilkay Gundogan and Lars Bender, while captain Philipp Lahm is suspended.
However, Flick was quick to praise the squad depth at the their disposal, insisting: "Even despite the missing players, we can handle any absence because of our team’s strength."
Germany are looking to make it three wins from three when they take on Giovanni Trapattoni's men, but the former Bayern Munich midfielder has warned his side that they must be at their best defensively if they are to leave Dublin with a positive result.
"Our focus is absolutely the defence. We have been working on the basics which at times have not worked that well in the past," he added.
"Defence starts from attack and we need to be compact. We need to have order and move well. Our offensive players will also need to do a lot of defensive work."