There was already a failed attempt at an OVA based on Mystery of the Emblem: Book 1, the game which was later remade as Fire Emblem: Shadow Dragon. It resulted in only 2 of the planned 30 episodes (For Book 1).
However, elements from the anime had influence on Shadow Dragon. It's likely because of this anime Nintendo specifically sought out Masamune Shirow (Creator of Ghost in the Shell) to produce the graphics, artwork, and cutscene CGs for Shadow Dragon and Mystery of the Emblem: Heroes of Light and Shadow (respectively). And yes, he did in fact end up having most of the artistic direction control for the Marth remakes, and Echoes is specifically made to pay homage to the artstyle of FE11/12 due to Echoes taking place between and being directly connected to 11 and 12 (as a full trilogy).
It also was the source of FE11's design for Cornelius, who was previously a completely unseen character in FE1 and FE3, and gave the idea for the prologue of FE11 even though the Prologue is not a straight adaption and is, instead, a new scenario that actually contradicts the OVA and is merely similar in setting.
Echoes itself also is being produced by a relatively famous anime studio:
Studio Khara. Fire Emblem Echoes will be Studio Khara's
first ever work on a video game of any sort, so Fire Emblem is starting to have pretty strong (legitiment, not just "oh it looks like anime") ties to anime as an industry once again.
In other words, the chances of Studio Khara making a Fire Emblem OVA again to try and do-over the failed one
are now pretty ****ing high. And here's how it's most likely going to play out if it does happen-
Studio Khara is most likely to produce the anime, and the anime will be an OVA adaption of FE11- Shadow Dragon- as the game is a remake of FE3 Book 1- in other words, a do over of the first OVA, but actually being finished and being based on the updated DS remake instead of the original version.
Then,
a tie in adaption of Fire Emblem Echoes would be the next logical step, followed by
an adaption of Mystery of the Emblem: Heroes of Light and Shadow/FE12, to form a trilogy of OVAs focusing on Archanea, Valentia, and the story of Marth and Camus.
This seems exceptionally plausible due to the upcoming Fire Emblem Echoes.
After that, if the OVA is successful, it's plausible they'd adapt the Jugdral/SNES games next, followed by the GBA games (7, 6, and 8, in that order) and Tellius. Then they'd possibly adapt Fire Emblem Awakening, and Fates is where it's anyone's guess due to the multiple path approach to it- perhaps we'd get 2 parallel OVAs, one for Birthright and one for Conquest, followed by an OVA of Revelation?