User blog comment:Skeith9/Heroic Spirits Speculation/@comment-24967786-20140521135716/@comment-24754018-20140521222358

If you really wanted Loki, you could probably try a Fate/Extra profile, that setting is slightly looser due to the Moon Cell being somewhat different than the Fuyuki Grail (at least based on my somewhat lacking understanding of the Extra setting). They allowed Tamamo (Playable Caster), who was like a diluted aspect of Amaterasu or something.

But yeah, under the main series, summoning divine spirits is specifically out of bounds:

"While full gods cannot become Heroic Spirits, demi-gods and those who lose their divinity like Medusa and Chiron are applicable."

I suppose you could twist the legend abit to make Loki lose his divinity or something though.