IL -

Today I learned from a coworker that my director (a female) had said I have a problem reporting to a woman. This is an entirely false statement as I have had very successful relationships with women supervisors in the past, some of whom still reside in my place of employment and would vouch for me. I feel this is slanderous and can unfairly impact my chances for advancement now and in the future. By the way, I am a male. Your thoughts?

How uncomfortable. You may wish to have a confidential and diplomatic conversation with your director. During the conversation, make sure that you do not make accusations as they will make her feel uncomfortable or even upset, whether they are true or not.

Perhaps you can phrase it as, "someone just told me something that I was upset by and that I know is not true" Then, tell her what was said. Ask her how to handle this coworker, etc.

If you believe that she continues to make such comments, you can go up the chain of command or to your HR department to report it. A pattern of such comments could be sexual harassment. (One such comment would not necessarily be seen as harassment.)