The traditional list of references is another casualty of changing résumé standards. You certainly need a list of references – keep them as up-to-date as the rest of your résumé. Just keep them on a separate sheet. When a prospective employer is looking at your résumé, they're several steps away from the point where they care about references. It's a waste of space. When they want to check your references, they'll let you know.
While you may have thought you'd found a clever way to save space by writing, "References available on request" on your résumé, you're not exactly telling your employer anything they don't know. Of course your references are available on request. That's how this whole process works. Don't bother putting that on your résumé.