Well let's look at all of the Summons that are, could be, or could have been primals in the Final Fantasy universe, shall we? Separated into lists.
Traditional Summons:
Alexander - Not Announced yet.
Atomos - Currently residing in Labyrinth of the Ancients.
Bahamut - Elder Primal, not able to be fought yet.
Behemoth - Fightable during FATE "Behold Now Behemoth" and its follow-up, "He Taketh It with His Eyes". Also appears as a mount and as a minion.
Carbuncle - Available as a Summon for Arcanists in "Topaz" and "Emerald" form. No announcement or sightings of "Ruby", "Pearl", or "Diamond" forms.
Catoblepas - Fought as a Boss in Halatali - Hard Mode.
Diabolos - Fightable as the final boss of The Lost City of Amdapour
Fenrir - No announcements, but has been sighted in the Final Fantasy XIV: A Realm Reborn Collector's Edition Artbook.
Gilgamesh - Fightable during the "Battle on the Big Bridge" trial.
Golem - A common enemy found across Eorzea, most notably found in The North Shroud and Outer La Noscea.
Ifrit - Primal, fightable in the normal, Hard Mode, and Extreme Mode "The Bowl of Embers" Trials.
Ixion - Not Announced Yet
Kirin - Not Announced Yet.
Lamia - Not Announced Yet.
Leviathan - Primal, Fightable in the Hard Mode and Extreme Mode "The Whorleater" Trials. (There is no Normal Mode)
Lich - Not Announced Yet.
Maduin - Not Announced Yet.
The Magus Sisters - Not Announced Yet.
Midgardsormr - Guardian of the Aetherial Seal at Silvertear Falls. Its death during combat against Garlean Airships resulted in beastmen able to summon Primals. While not a primal, its power is comparable to the Primals themselves.
Odin - Fightable during the FATE "Steel Reign".
Ramuh - A Primal worshipped by the Sylphs.
Shiva - Announced as a Primal at a later date.
Siren - Fightable as the final boss in Pharos Sirius.
Tiamat - Not Announced Yet.
Titan - Primal, fightable in the normal, Hard Mode, and Extreme Mode "The Navel" Trials.
Ivalician Summons:
Adrammelech, the Wroth - Not Announced Yet.
Belias, the Gigas - Referred to as an Elder Primal during the Level 50 Summoner Job Quest. Using multiple Summoner Soul Crystals, a Belias-Egi was summoned.
Chaos, Walker of the Wheel - Not Announced Yet.
Cuchulainn, the Impure - Not Announced Yet.
Exodus, the Judge-Sai - Not Announced Yet.
Famfrit, the Darkening Cloud - Not Announced Yet.
Hashmal, Bringer of Order - Not Announced Yet.
Mateus, the Corrupt - Not Announced Yet.
Shemhazai, the Whisperer - Not Announced Yet.
Ultima, the High Seraph - Not Announced Yet.
Zalera, the Death Seraph - Not Announced Yet.
Zeromus, the Condemner - Not Announced Yet.
Zodiark, Keeper of Precepts - An Elder Primal worshipped by the Ascians, whose power is said to rival that of Hydaelyn.
FFIV-Exclusive:
Asura - Not Announced Yet.
Mist Dragon - Not Announced Yet.
FFV-Exclusive:
Syldra - Not Announced Yet.
FFVI-Exclusive:
Bismarck - Not Announced Yet.
Crusader - Not Announced Yet.
Lakshmi - Not Announced Yet.
Seraph - Not Announced Yet.
Valigarmanda - Not Announced Yet.
Zone Seeker - Not Announced Yet.
FFVII-Exclusive:
Hades - Not Announced Yet.
Knights of the Round - Not Announced Yet.
Kujata - The Final Boss of the Marauder Class Quest Chain.
Typhon - No announcements, but has been sighted in the Final Fantasy XIV: A Realm Reborn Collector's Edition Artbook.
FFVIII-Exclusive:
Cerberus - No announcements, but has been sighted in the Final Fantasy XIV: A Realm Reborn Collector's Edition Artbook.
Doomtrain - Not Announced Yet.
Eden - Not Announced Yet.
Pandemona - Not Announced Yet.
Quetzalcoatl - Not Announced Yet.
FFIX-Exclusive:
Ark - Not Announced Yet.
FFX-Exclusive:
Anima - Not Announced Yet.
Valefor - Not Announced Yet.
Yojimbo - Not Announced Yet.
FFXI-Exclusive:
Garuda - Primal, fightable in the normal, Hard Mode, and Extreme Mode "The Howling Eye" Trials.
FFXIII-Exclusive:
Brynhildr - Not Announced Yet.
Hecatoncheir - There is a beastman race named Hecatoncheir that worked as slaves in the Copperbell Mines. However, they bear no resemblance to the original and are therefore considered to be completely unrelated.