I get the impression that any time you have a level where you are receiving information from a senior executive about what another senior executive said in a private conversation with him, you should be a bit more up on how to deal with things like this than you seem to be. And you more than likely have had more dealings with the type of situation where this person might be concerned about your being in supervision over or working closely with white male co workers. If you don't think private conversations like this have happened before during your career, you're not very far up the ladder yet.
So I would strongly suggest, though there is no legal question here, and you did not tell us your state (U.S. law only) that if you are so pushed out of shape that you definitely begin seeking another job and simply go forward from here. My six thousand dollar question is, tell who? You say, 'Should I tell them or wait till I leave?" My question is, Tell who what?
If the person who said this is a senior executive, and he made this statement in a private conversation with someone, you might succeed in getting the person who told you about the statement fired. But it would doubtless not go further, would not accomplish much, and you're going to go out with a lot of issues leaving a bad taste behind you in the mouths of your former employer.
If you try to begin by telling the EEOC, their first question would be to the employer if this has happened. And if it did, and you were offended deeply and thought you were being discriminated against...though apparently nothing has happened yet, you don't even mention whether you did or did not get the job assignment. Even if you play them the voicemail, (by the way, hope you're in a one party recording state! ) the company will deny that any racial discrimination took place, and that you had not discussed the situation with them at all before leaving, so they were unaware that you felt there had been a problem.