Can I install storm door on the door frame?
A little more info is needed to give any good answer. I can see what would be considered "brick mold" looks like it is extruded aluminum. The frame that you point to looks like it could be painted wood, but the angle at the top tells me it may not be wood at all, or perhaps it is clad in aluminum ?? 

Typically the storm door jamb screws into the face of the brick mold, just as you may already know. If the surface you point to is painted wood, the storm door jamb can go there, provided there is enough room at the door handle to not interfere with the operation of the new storm door and likewise the original door.

The angle at the top I referred to earlier may complicate the storm door jamb install.