When trying to set the Member Policy or Owner Policy on a new Access or Admin Role to "Users who are members of admin role <role name>" and clicking the Browse button and then searching for roles, no admin roles are returned, either when searching for a specific role by name, or with a wildcard search.
The user does not have an Admin Role assigned allowing him/her to manage Admin Role objects.
Ensure that the user has been assigned an Admin Role with a member policy that includes a scope rule allowing them to manage Admin Role objects.