GM (general manager) hires all players. Coach only coaches.
That's different from college football, where head coach recruits the players/team. That's why 49er's head coach went back to college (Michigan), because he had much more power in college football.
Broncos GM fired the head coach, because they did not get to SuperBowl this year (2 years in a row) and he felt the reason was coach did not motivate the team. His goal is to make sure they go to playoff next season, otherwise he himself would be fired.
I bet he (GM) will keep Manning. Without Manning, playoff can not be guaranteed. He works for his own paycheck.