"Likely" is different from "beyond a reasonable doubt" -- given the myriad cultural and historical baggage surrounding homosexual activity and homosexual activity (not to speak of bisexuals!) and the nature of medieval and early modern gossip it's incredibly difficult to make statements about historical figures' sexual preferences that absolutely no one in academia will argue with. But for historical monarchs where there's substantial positive evidence of same-sex sexual affinities, King James VI & I of Scotland and England is a likely candidate. You might like this thread:
But the very question suggests some of the problems for historians in discussing historical sexual preference -- how does one distinguish sexual preference from social preference? When should the male favorites of a male monarch be understood as at least potential lovers, or the female favorites of a female monarch? Can we talk about male favorites in similar terms to (female) mistresses? When is the stigma of same-sex sexual activity used by monarchs' contemporaries or by later historians to discredit the intimates of certain monarchs, especially ones of common birth or simply insufficiently high degree? (George Villiers, Piers Gaveston, Robert de Vere, Henri III of France's mignons, Sarah Churchill, and so on -- all defined by their relationship to same-gender kings and queens.) What of monarchs with opposite-gender favorites who for various reasons could not easily fit those favorites into the role of mistress or lover, like Elizabeth I of England? What about one-night stands, courtesans and kept boys who did not rise to the level of political confidantes, and so on? What about monarchs who were distinguished not so much by same-gender intimacy but by cross-gender role identification? It's a really messy area of study. But at the same time, if I had to point to one and only one monarch, King James VI&I is a handy dandy candidate.
The FAQ on Gender and Sexuality has some nice reading on sexual orientation in past cultures.
/u/Yazman wrote a fascinating answer about speculation over the sexuality of al-Hakam II and I've been trying to find an older answer on to what extent sexual activity compared to the religious ideal in Medieval Islamic societies but no luck.