Sewer drain question

I'm tiling my floor in the basement bathroom. When I removed the toilet, I noticed that the flange is offset from the sewer drain. Only about half of the sewer drain is visible (which probably explains why the old toilet never flushed very well). It appears as though somebody put an angled piece of rubber or something to direct the water that isn't over the drain, into the drain (I hope that makes sense). It's also evident that some of the concrete around the drain has been removed and patched back. My question is, would this be a relatively easy fix? Chipping and replacing the concrete is not a problem. My concern is the fact there is a patch there already and maybe there is a problem that won't allow the flange to line up with the drain. I also bought a new toilet and don't want the problem of it not flushing properly. Any feedback would be greatly appreciated!

I photo is attached.

Post a picture with the wax ring that has the plastic horn as part of it removed from the flange. The wax ring will probably come off leaving that plastic funnel in there but it too needs to come out. We can see the flange better at that point.

You could try a 3" offset flange....

flange

Your picture is too distant and does not have enough detail for us to see what you are talking about. The picture, as I see it, shows the flange centered on the riser pipe. What are the green pieces of plastic?

Thanks for the replies. Here is a closer picture without the wax ring. Hopefully it's a little bit clearer. It's definitely not centered over the drain. As far as the "green pieces of plastic", I think it's just green gunk stuck to the drain. Thanks again!

Looks like an off-set floor flange.....

flange

That is an offset flange, but since it appears to have a smooth transition to the pipe it should not create the problems the oval ones with a ledge do.