Melt 4 tablespoons of butter in a saute pan over medium high heat. Saute mushrooms, onion, and celery for 5 minutes, stirring frequently. Stir gently into the dry stuffing mix along with the cooked wild rice to evenly distribute.
Heat chicken broth, wine, and remaining 6 tablespoons of butter in a small pan until the butter is melted and the liquid is simmering. Pour over stuffing mixture, and stir until the stuffing is evenly moistened. Place into a baking dish.
Bake at 350 for 20-25 minutes, or until heated through and the top is lightly golden brown.