Let's start by ensuring we have a common understanding of Distribution Statement C:

DISTRIBUTION C. Distribution authorized to U.S. Government Agencies and their contractors. (reason) (date of determination). Other request for this document shall be referred to (controlling DoD office).

In the situation described in the question, the controlling DoD office would most likely be an organization with the Department of the Navy.

For DoD distribution statements info, see URL https://discover.dtic.mil/wp-content/uploads/2018/09/distribution_statements_and_reasonsSept2018.pdf

DOMESTIC:  With regard to release of Distribution C documents to prospective domestic U.S. contractors or subcontractors prior to award, no foreign release approval is required.  Consult your Contracting Officer -- who will comply the FAR/DFARS regarding transmission, handling and safeguarding of Controlled Unclassified Information (CUI) -- to obtain detailed information on how this is accomplished in practice.

Since the questioner is in the Department of the Navy (DON), here is a DAU perspective on the DON process for making a decision to release a Distribution Statement C CUI document to prospective foreign contractors, subcontractors, or suppliers (entities):

- Obtain a DON decision that authorizes release of the CUI document(s) to one or more prospective foreign entities.

- Consult your Contracting Officer on how to implement the transfer of the CUI considering the policies and best practices described in the ACQuipedia Article "International Acquisition - Export-Controlled (EC) Controlled Unclassified Information (CUI) Release to Foreign Industry during DoD Contracting" at URL https://www.dau.mil/acquipedia/pages/articledetails.aspx#!250

A final caveat -- while the above advice is based on overall DoD policy and practice and our DAU-level understanding of Navy policy and practice, the actual decision and implementation authority resides with the Department of the Navy at the SYSCOM or Navy International Programs Office.