Astrophysical Journal: Magnetic fields are the primary driver of the plasma thermodynamics in the upper solar atmosphere, especially in the corona. However, magnetic field measurements in the solar corona are sporadic, thereby limiting us from the complete understanding of physical processes occurring in the coronal plasma. In this paper, we explore the diagnostic potential of a coronal emission line in the extreme-ultraviolet (EUV), i.e., Ne viii 770 AA to probe the coronal magnetic fields. We utilize 3D 'Magneto-hydrodynamic Algorithm outside a Sphere' (MAS) models as input to the FORWARD code to model polarization in Ne viii line produced due to resonance scattering, and interpret its modification due to collisions and the magnetic fields through the Hanle effect. The polarization maps are synthesized both on the disk as well as off-the-limb. The variation of this polarization signal through the different phases of solar cycle 24 and the beginning phase of solar cycle 25 is studied in order to understand the magnetic diagnostic properties of this line owing to different physical conditions in the solar atmosphere. The detectability of the linear polarization signatures of the Hanle effect significantly improves with increasing solar activity, consistently with the increase in the magnetic field strength and the intensity of the mean solar brightness at these wavelengths. We finally discuss the signal-to-noise ratio (SNR) requirements by considering realistic instrument designs.