Murmur a suggestion (9)
I believe the answer is:
undertone
This clue is a double definition.
'murmur' is the first definition.
(I've seen this in another clue)
'a suggestion' is the second definition.
(thesaurus)
(Other definitions for undertone that I've seen before include "Low or subdued voice pitch" , "Quiet way of speaking" , "Implicit meaning" .)