This is in response to the OP's recent reference request.

It sounds like the reference you seek may be John Milnor's paper 

Construction of universal bundles. I.  Ann. of Math. (2)  63  (1956), 272–284. 

Milnor constructs a universal bundle whose fibre is the space of "simplicial loops", by analogy with Serre's loop space fibration. It turns out that this fibre is now a group.