Durin's Bane

[Insidious Rex]

So I rarely actually talk Tolkien here anymore it seems but a I was asked a question recently for which I couldnt immediately reply with an answer so I figured Id come here to ask the experts...

Why didnt Sauron ally with the Balrog in Moria? Was it just because he couldnt control a fellow Maiar and this was all about being in complete control of his minions (orcs, trolls, nazgul, etc.)? Or was it something else? I mean seems like an awesome ally to have in his quest to defeat the forces of good. I cant imagine he didnt know it was there because even if he hadnt had suspicions after the Dwarves were routed by the creature and abandoned their underground kingdom completely AND the Silvan Elves were freaked out enough to leave their homeland even, then once he sent orcs and trolls to block the Misty Mountain passes they would have reported back essentially: HOLY CRAP! THERES A MONSTER IN MORIA! HELP! Or maybe he did communicate with the Balrog and asked him kindly not to kill his orcs and trolls that will be sharing his dark lair or this was just an unspoken understanding between the two evil entities. And Ive heard folks say its no coincidence the creature awoke when it did despite the insistence that it was greedy Dwarfs mining too deep that awakened it because it appeared in the EXACT same year that the Nazgul returned to Mordor.

All this aside, why wasnt there a direct and obvious alliance between Sauron and the Balrog? Kind of like what there was in Angband with Morgoth although granted Morgoth was Ainur.