An Etymological Dictionary of the German Language/Muff
Muff (1.), m., ‘muff,’ ModHG. only; from LG. muff, Du. mof, ‘muff,’ E. muff; a modern Teut. word connected with Fr. moufle, ‘mitten,’ MidLat. (even in the 9th cent.) muffula. The origin of the cognates has not yet been determined; they are generally connected with MidHG. mouwe, ‘sleeve.’
Muff (2.), ‘mould,’ MidHG. only, allied to Du. muf, ‘musty, moist, mouldy’; late MidHG. müffeln, ‘to smell bad or rotten.’ With these are connected the widely-diffused Rom. cognates, which are said to have originated in the G. words: Fr. moufette, ‘firedamp (in mines),’ Ital. muffo, ‘mouldy.’