Quote from mcknis
I have not been given the opportunity to serve in the manager role previously, but these individuals must have seen something in me to raise this point.
No not necessarily, they could be asking anyone with a pulse. Or, the people who approached you with the idea of management were just blowing smoke up your bottom to get you hooked on working for that company/department. Or the person who is retiring is being forced to do so and actually has no say or authority in who will be his/her replacement. Or there may be a more popular candidate in the mind of others, who is likely to get the job over you and every one else but that was never told to you during your interview.
On the other hand, who cares? Do you want the position or not? If so, do your research.
Research includes talking to people and feeling out the politics/behind-the-scene-dynamics of the department/company as well as the players involved, the day-to-day tasks and life of the job, the expectations of new managers, and the support system and training you can expect to receive after you start. After you have honestly gotten a good picture of the position, approach the right person (preferably the one who is retiring) with your interest. Good luck!