Is Magnetic Force Conservative or non conservative in nature?

forcefield is conservative, if its rotor vanishes, in your case that would mean that:
 
rot(B) = 0.
 
if you look at Maxwell's equations, it holds that: rot(B) = µ_0*j + µ0*e0*dE/dt
(where µ0 ... magnetic constant, e0 ... vacuum permittivity, dE/dt ... in this case the PARTIAL derivative of your electrical field, j ... your current density).
 
So, I would say, no, the magnetic force field is in general not conservative