An Etymological Dictionary of the German Language/Annotated/mögen
mögen, verb, ‘to like, choose; may,’ from Middle High German mugen, mügen, Old High German mugan, earlier magan, preterite present, ‘to be able, have power,’ Gothic magan; a common Teutonic preterite present with the Old High German and Middle High German meaning, ‘to be able, have power,’ as it appears in the Modern High German abstract form Macht, and in the compound vermögen; Anglo-Saxon mœg (plural magon, preterite mihte), whence English may (preterite might). The Teutonic stem, mag (mug), from pre-Teutonic magh, is most closely allied to Old Slovenian mogą, mošti, ‘to be able, have power.’