We report the tunneling current behavior of magnetic-ferroelectric-superconducting heterostructures for multistates non-volatile random access memory (NVRAM) elements. A heterostructure of La0.67Sr0.33MnO3 (LSMO) (50 nm)/PbZr0.52Ti0.48O3 (PZT) (5 nm)/Bi-Sr-Ca-Cu2-OX (BSCCO) (100 nm)/LaAlO3 (LAO) architecture was fabricated by pulsed laser deposition technique. The tunneling effects were investigated well above and below the superconducting phase transition temperature of the BSCCO bottom electrode. A divergent current and conductance paths were observed for polarization up and down direction above the coercive field of the ferroelectric tunnel barrier. This behaviour was significant below Ts where the moderate effect of the external magnetic field was also observed on the tunneling current. The dynamic conductance G(V) data fitted well with Brinkman's model for both polarizations up and polarization down states which suggest the presence of large tunnel electro-resistance.