Do you have the proper light conditions to grow turf? If not, turf will never succeed. If there is so much foot traffic that turf can't survive, you need to install a paved path of some sort. Pavers on a proper gravel/sand base would be fine. If you want to use gravel mulch as a path that is OK, but will require a restraining edge to keep the gravel in place. You can use woven polypropylene landscape fabric below the gravel path in order to help stabilize it. Explore Google Images for examples of how this is done.

Gravel is rarely a great choice in muddy areas. It will simply sink into the mire, even with landscape fabric. Best to either redirect the source of the soggy bottom, find a way to drain it, or regrade the area so water won't congregate there. And then maybe, if there is enough sunshine each day, maybe the turf will establish itself. I wonder about that based on the moss.

I meant to mention ... many times people describe situations and their description often leaves out important facts that show up just as soon as we see a picture. Don't hesitate to post a picture of the subject area. Make sure it is not a close-up so we can see the surroundings and context.

Sorry I don't have a turf issue. That was a mistake. For now I want to avoid a costly time consuming project like pavers. We get a lot of rain and the area is on the north side of the house so shaded and doesnt get much growth and the foot traffic doesnt help.

"... on the north side of the house so shaded ..." and "... I don't have a turf issue ..." is a contradiction, so clarification/details needed.

If it gets foot traffic, gravel is a poor choice to my mind unless as Yardvaark recommends that it is restrained by an edging and underlain by geotextile fabric, as well as what Kiminpl commented on, dry enough soil that it won't sink. It would also need to be a type of material such as what is referred to as knit-pack around here, crushed rock (granite in my area) that has very fine, fine, and medium pieces so that it all knits together and is a stable surface that doesn't shift when it is walked on or get kicked into the surrounding grassy areas (where it has the potential to get thrown by the mower.) I am not certain that I see this as easier or less costly to create and maintain than digging down and adding sand as a bed for a set of 2'x2' paver slabs.

I think you and Yard are talking at cross-purposes about the turf. Your turf issue is that grass won't grow.

As mentioned above by others, a photo (along with some idea of where in the world you are) would help considerably since we are operating blind here. I also think that before doing anything I would add the gutter and seed in shade-tolerant grass to see if that takes care of the problem as it would be the easiest solution.

Ill try to get some pictures and post. In the meantime I live in the Pacific Northwest about 30 miles east of Seattle in the skykomish river valley.

Pictures make such a difference in understanding. A small area with traffic like this needs to be hard surface or, at minimum, retained granular (gravel) surface.)

It's a small enough area that I would consider a walkway of large pavers; they make 2'x2' ones, and IMO would be easier than smaller ones.

The only issue with large pavers is I'd have to move a lot of dirt and then make a base more labor intensive and probably more expensive as well. Lot more level will have to be done also. I'll have to measure and then do a compare. Thanks.

Yaardvark what do you mean by hard surface? Concrete? What does 'retained' gravel mean?

As mentioned earlier, gravel can't be easily used as a walk unless something surrounds/retains its edge. Otherwise the gravel bleeds into the adjacent soil with the two mixing and gravel scattering everywhere. To prevent that, it has to have some kind of metal, concrete or wood frame surrounding it.

Hard ... yes, any typical paving material: concrete, brick, asphalt, pavers, etc.

A raised stone path perhaps ? image from a temple garden in Kyoto.