Repair shower drain leak
Possible? Yes. Easy? Maybe not.

If you look inside of the flange, there is what appears to be a raised ridge with some breaks in it, dividing it into 4 equal sections. That is a way to latch onto that flange with a special tool to hold and unscrew it from the other half of it that is below your shower pan. A good plumbing store or hardware store should have a selection of different versions of tub / shower drain removal tools, yours will likely look something like this:

Or this:


Before you go to look for one though, find a piece of cardboard and cut it to fit across two of the gaps so that you know the width of the wrench spacing.

Then once you have the wrench, getting the part to unscrew is not going to be easy, because it appears as though someone used a hard putty under the flange (which is likely why it is leaking); it was supposed to be a softer type of "plumber's putty" that never really sets up hard, for this exact reason. If you have an Exacto-Knife, run the blade around the edge of that flange seal area to try to loosen it up a little. If it seems soft, that's good. If it's hard and crusty, you may have a big problem.

Here's what the entire assembly looks like to give you an idea of what you will be trying to do.