Nothing confirmed until 4.0 goes live and people can play the class (or unless Fanfest gives us some lore info on the job), but...
The running theory is that Red Mage is linked to Sharlayan for a number of reasons.
Lore: Lorewise, Black and White Magic has been taboo since the War of the Magi resulted in the Calamity that flooded Eorzea. Red Mage has been stated to use Red Magic; a combination of White and Black Magic. For this to be possible, Red Mage would have to of developed outside of Eorzea, yet had connections to Eorzea, which is the origin for White and Black Magic. There has been a running theory for a while used to explain the magical feats of the Scions and other Sharlayans, which states that Sharlayan was founded by dissident White and Black Mages during the War of the Magi, who fled Eorzea, founded Sharlayan together, and put the focus of their studies on Learning and Knowledge, rather than power and ambition.
Even assuming that this theory is untrue, the fact remains that Sharlayan remains the (currently) most logical place for Red Mages to develop, given the Sharlayan drive for learning, not dissimilar to how they're bringing back Summoners. Its a highly magical society that doesn't scruple to employ or delve into magic others consider forbidden (look at all the Bound-Voidsent Guardians in the Great Gubal Library, for example).
Aesthetic: The reveal for Red Mage showed us (presumably) AF gear which has a distinctive Sharlayan flair to it when compared to other Sharlayan fashions such as the updated outfits of the Scions, the gear from the Great Gubal Library (Normal), and the Tomestone of Scripture set: Shire Gear. Likewise, the Magicked Crystal Medium offhand is noted to float, and the only other class to have a weapon which floats, is Astrologian, which also comes from Sharlayan.
Alisae: As of Patch 3.4, Alisae's development in combat reveals a very Red Mage like combat style of combining swordsmanship with spellcraft.