Balrogs and Sauron

[Jurion]

Do you remember what the emmisary of Sauron said to Dain, King of the Lonely Mountain:

Find it (The One Ring), and three rings that the Dwarf-sires possesed of old shall be returned to you, and the realm of Moria shall be yours forever. (II, The Council of Elrond)

This suggests that if Sauron knew of the Balrog in Moria, he was also in control of him.