The Collaborative International Dictionary of English v.0.48:

Murmurer \Mur"mur*er\, n.
   One who murmurs.
   [1913 Webster]

WordNet (r) 3.0 (2006):

murmurer
    n 1: a person who speaks softly and indistinctly [syn:
         mutterer, mumbler, murmurer]