[Nilpaurion Felagund]

It may not have been subservient to Sauron, but I think that at the least the Balrog was in league with him. And I think that it says in the text that 'Sauron was putting out the call to all evil things.' Surely the Balrog would have responded in come fashion. (alatar)

Let us not forget that the Balrog and Sauron both were servants of Melkor. There is no point whatsoever to believe that they are now allies or something. They fell under the dominion of Melkor because he was more powerful, being a Vala and them being Maiar. The difference in power between Melkor and Sauron (or the Balrog) was way bigger then the difference of power between Sauron and the Balrog. Gandalf says, when in Moria, that he has met his equal in the Balrog. And Gandalf is only little less than Sauron.
The fact they both served under Melkor and both were high in his esteem seems to make them pretty equal. Now that Melkor is in the Void, I don't believe any Balrog would be in league with Sauron or be helping him altogether. (lathspell)

No, the Balrog and Sauron weren't on the 'same team' because that would mean the Balrog was on Sauron's team, and no way would an elfbane like that kneel to a peer. Personally, I think the orcs referring to the Balrog with cries of 'Ghash' were not all that unalike to referencing Saruman as Sharkey or referring to anything back home as 'Lugburz' wanting a prize. Those orcs may have been sent to Moria by Sauron a few centuries before to investigate and inhabit the place, but it was clear that Durin's Bane was in charge, and they kept clear of him. However, if he felt the need to use them to send message back and forth to Dol Goldur, there's no evidence of it happening. While Sauron maybe of all people knew the shadow of Moria was the Balrog, the Balrog seemingly, knowing full well Sauron was a higher up, didn't care to leave Moria for any reason. It was . . . "His realm" and any orc there was there by his leave. I wonder if he had declared himself Lord of Moria . . .

So anyway, regardless of being aware of eachother I don't think there was a lot of talk between the Balrog and Sauron. After all, the Balrog would probably take Sauron for a traitor after going AWOL when Huan ripped his throat out and leaving Morgoth without his most devious schemer during the War of Wrath. If anything, Durin's Bane probably didn't really like Sauron that much anyway, thinking him nervy to take the title of 'Dark Lord'. (Keep')

(Both quotes from Wielding the Flame of Anor by Keep')