Full Idea
The heart of the problem is Frege's assumption that predicates have Bedeutungen at all; and no reason is at present evident why someone who espouses Frege's notion of object is contrained to make that assumption.
Clarification
'Bedeutugen' is usually translated as 'references'
Gist of Idea
We can accept Frege's idea of object without assuming that predicates have a reference
Source
Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iv)
Book Reference
Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.17
A Reaction
This seems like a penetrating objection to Frege's view of reference, and presumably supports the Kripke approach.