Software developer to Engg manager

I am a decent software developer with 12 yrs of experience and want to move to engg management. Is it possible to do so while switching job? I don’t see that happening in current company which is I believe is easy and ideal way to move into mgmt.

I do not have managerial experience but in my current company I see I can contribute on those fronts but someone else is already being considered for the managerial position. I am working in a product company. Can moving to service company give me opportunity to move to management? Is it even a good idea?