Cook wild rice according to package directions; drain and set aside.
Melt butter in top of a double boiler over simmering water; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over boiling water, stirring constantly, until thickened and bubbly. Stir in salt and cream cheese. Remove from heat.
Grease a 1 1/2-quart casserole. Spoon half of wild rice into dish; place half of mushrooms on top of rice, and spoon half of cream cheese sauce evenly over mushrooms. Repeat layering procedure. Bake at 325° for 30 minutes. Serve hot.