Are we allowed to provide a list of companies that submitted a response to our market research?

I've had this happen before. I told the vendor "No" because I had not advised in the sources sought notice that the names of companies that responded would be released. If you do decide to do so, then I would release the information publicly.

creyes814 said:

Are we allowed to provide the list of companies to a prospective vendor that have submitted a response to our market research?  A vendor asked if he could have the list of companies.

You may want to visit with your FOIA office or representative.  By experience there is probably a relation to FOIA Exemption 4 but as it goes details may count.  Just a suggestion in case the requester presses for the information.

If you do say "No", be sure to send them to your office's Small Business Program Manager for the established guidance in prospecting opportunities.

This might help answer your question. It mentions making those firms expressing an interest in respond to a Sources Sought announcement available to the public. 
https://www.aptac-us.org/sources-sought/

Pre-electronic contracting, the USACE used to make lists of firms that requested copies of construction contract solicitations available to those firms requesting a list in order to provide subcontracting opportunities.

im not familiar with the current methods and procedures.

creyes814 said:

Are we allowed to provide the list of companies to a prospective vendor that have submitted a response to our market research?

Yes, unless you promised not to release their identities. See FAR Subpart 5.4, Release of information.

l do not know of any statute, regulation, or policy that prohibits disclosure of the names of firms that have merely expressed an interest in an upcoming procurement.

FOIA exemption 4 does not preclude the release of such information.

https://www.justice.gov/archives/oip/foia-guide-2004-edition-exemption-4#:~:text=Exemption 4 of the FOIA,government and submitters of information.