I am guessing this might just become like the Mephisto joke from the WandaVision series if MCU goes in some different direction, but at this point, there are strong hints of who might be the Loki Variant. And the answer to that is
Lady Loki. In the comics, Loki is gender fluid, and if you take a closer look at when Owen Wilson is reading Loki's file - it says
SEX: FLUID.
MCU never mentioned it, but this is the first confirmation that he is gender fluid. The second hint is in the credit scenes. There are two stunt doubles for Loki and its variant. The Variant double is, however, a woman.
In the comics, Loki becomes Lady Loki and works for an organisation founded by Norman Osbourne named Cabal. However, she has no relation to the TVA as far as comic lore is concerned. So if the variant is indeed Lady Loki, this will be an original story.