While we don't have a good enough pic of the case to ID it, from what I can see this is a cheap, VERY old design, where having a fan mount was more of a token gesture than an effective way to get air in, not because of the fan size but rather that the entry in front of it, is 90% sheetmetal and 10% perforated holes.
This type of case design was meant for an era when systems produced about 100W heat max. I wouldn't use it at all, but if you insist on using it, then it needs some carving done.
First, assess whether that front sheet metal wall of the case is thick enough to not vibrate if you remove and discard the fan box. That box does nothing good otherwise, even holes the fan away from the front wall of the case (most likely) so what little air it might've pulled in through the few tiny holes there were, isn't happening because there is no seal against the front case wall so instead it recirculates air already in the case.
You'd be better off pulling that fan box off and cutting a hole for a 92mm fan. The original looks 80mm so 92mm should just fit. Next you may also need to open up the intake area in the plastic bezel in front of it.
Keep in mind that if your PSU has a fairly strong fan and your build isn't much over 150W, you don't necessarily need a fan there at all, just to cut out the hole so it has far less restricted passive intake. However I see what looks like the side of a double height video card, so odds are it can exceed ~150W and would be better off with the hole cut and a 92mm fan placed there.
Even if you want to stick with a smaller 80mm fan, that much more it needs a fan hole cut out and to ditch the box that holds it, meaning you also need to drill holes in the case front wall for the fan mounting screws.