I'm reading stalling's article "the augmented ideal in group ring" in Ann. Math. Studies 84(R. H. Fox memorial volume) In his final remark, he says that Milnor's link invariant could be interpreted by using Spectral sequence.(see Milnor, Isotopy of links, Algebraic geometry and topology, Princeton press)

Are there anybody who knows about further advances in this story??

specificspectral sequence devised in that same paper by Stallings. I'm not aware of any reference about this. A relevant discussion is on page xiv in the introduction to a recent book by Roman Mikhailov and I.B.S. Passi. – Sergey Melikhov Jan 21 '11 at 14:07