By the description, it sounds like you have given it a good look and know that it is not an algae bloom? Not tiny little green dots too small to see until there are lots of them?
So if it is small bits of debris, then we should move to the filtering. If the parts are suspended and not being taken out by the filters, there might be two causes. One which might be overlooked is when you have fish who do a lot of bottom stirring so that there is a constant flow of debris kicked up.
Another and more likely might be that your filter cleaning routine is not good enough or the media used is not quite right.
To do a filter process check, we need to keep in mind that the nitrate is a result rather than something the filters remove. But if you have no ammonia or nitrite problems, the bio filtering is probably okay.
But the mechanical filtering may not be good. This can be poor choice of media, poor design of the filter, or it can be that the media is filled and unable to hold more debris. Poor media can let too much through. Poor design can let too much bypass the media. If the "look" of the water is somewhat better for a few days after cleaning, that would tell you that you need to clean more often.
If the debris is hanging out around the bottom, a look at a powerhead to get it moved to the filter intake may be the solution.
Just some suggestions to chew on?