There is some really great advice given so far on this thread. As a person who worked for the same company for 25 years, had some really great supervisors and a few not so great, and has witnessed all sorts of personnel changes, let me attempt to put this advice all together for you.
First, listen to @jerv. Think about if you really like this company. What about your current job? Do you enjoy it? Putting aside what the supervisor might or might not have said, do you like working with him? What about the other people in the dept? There are times where the current work environment is the side of the fence where the grass is greener.
Think about why you want this promotion. Is it to get out of a job that you currently don’t like? To move up the ladder? I’ve taken another job in a different dept. or accepted a promotion on numerous occasions. Several times, I have regretted it. While the job description may look good on paper as well as in the paycheck, it often means more hours, more work, less satisfaction, and in a few cases, leaving a good environment for one that awful under the surface.
Secondly, please listen to @marinelife. The co-worker who supplied this bit of gossip should never have done so. I wonder what her intent was. What did she expect you to do with this information?
There is a good chance that she misinterpreted what was said. I can imagine a supervisor saying in jest, “No, you can’t promote @Tachys because he/she is my right hand.” I would take a statement like that to mean, the person hiring would do well to get you on their team. As someone who has attended many meetings where this type of banter goes one, most managers, if they are good, want to help their direct reports move on if they so desire and are capable. “Blackballing” someone typically comes with the connotation that a candidate is not worthy. From what the co-worker said, this doesn’t sound like the case.
Third: Listen to @zenvelo. How are job postings made available? Without ratting out the co-worker, how about scheduling a meeting with your supervisor to discuss your future? Let him know that you are interested in career advancement, and would like his input and support. Let him know of areas that you are interested in and why. Ask what it would take to be considered for the next move. Having your supervisor on your side is one of the strongest weapons an employee can wield in office politics.
Without knowing how the hiring and promotion process works in this company, it is difficult to give advice. It is up to you to find that out. Does the company have an HR dept.? That is where I would start if I didn’t trust my supervisor.
And @CWOTUS also has a good point. Start thinking about who would be a good replacement for your current job and start grooming them to step in.
Please keep us posted on what happens. We are rooting for you and want to know what you decide to do.