Do you currently have a manager? Trying discussing this with your manager; perhaps you can work out a plan which can get you the experience needed to transition into a new management role. Your company may have a definition and data that they use when hiring a new manager; which would mean you have resources to understand what is expected of a manager and then determine what areas you have covered and what areas you need to develop.

Do/have you lead a tech team already (officially or not) at least as technical leader? Do/have you lead large architectural projects with many devs?