Mechanical Engineering versus Aeronautical Engineering

Absolutely! A good undergrad ME curriculum is excellent preparation for an MS and/or PhD in Aeronautical Engineering. As an ME undergrad you should take some courses in aerodynamics, fluid mechanics, etc., as well as some courses in structures (i.e, beam theory, plate theory, etc)., and some math electives beyond the basic undergrad requirements (partial differential equations, for example).

Hi there,
I am glad to see you are interested in pursuing Aerospace engineering master degree.
It works perfectly with an undergrad degree in Mechanical engineering.
With ME, you have already have
Fluid mechanics - the study of fluid flow around objects. Specifically aerodynamics concerning the flow of air over bodies such as wings or through objects such as wind tunnels (see also lift and aeronautics).
Dynamics and engineering mechanics - the study of movement, forces, moments in mechanical systems.
Mathematics - as most subjects within aerospace engineering involve equations and mathematical manipulation and derivations, a solid and comprehensive study of mathematics is required to enable effective learning in the other modules.
Electrotechnology - the study of electronics within engineering.
Propulsion - the energy to move a vehicle through the air (or in outer space) is provided by internal combustion engines, jet engines and turbomachinery, or rockets (see also propeller and spacecraft propulsion). A more recent addition to propulsion is ion thrust (or electric) propulsion.
Control engineering - the study of mathematical modeling of the dynamic behavior of systems and designing them, usually using feedback signals, so that their dynamic behavior is desirable (stable, without large excursions, with minimum error). This applies to the dynamic behavior of aircraft, spacecraft, propulsion systems, and subsystems that exist on aerospace vehicles. As aircraft flight control systems become increasingly complex, they can be studied as a separate module.
Materials science - related to structures, aerospace engineering also studies the materials of which the aerospace structures are to be built. New materials with very specific properties are invented, or existing ones are modified to improve their performance.
Solid mechanics - Closely related to material science is solid mechanics which deals with stress and strain analysis of
The components of the vehicle.

I have worked engineering professional job, and I did ask about being an aerospace engineer. The answer I have got is that the demand is declining lately.

I wouldn't worry about it too much, I personally encourage you to get master of aerospace engineering, you can always find jobs abroad if it's hard here.

Excellent