Do not pave as it will get worse....paved next to mine last year and discovered one of the run off areas for the septic tank.
Paving now gone.
I have planted water loving plants as the area is damp all year, small trees take a bit.
You can create a drainage areaor several by creating downward trenches, pouring water will show you run off and end in a gravel pit area. Several would help, starting spade depth, ending 4 spade depths if poss.