The stability of the viscous- viscoelastic fluid interface is theoretically examined when the heat and mass transfer is allowed from one phase to another phase. The viscoelastic liquid and viscous fluid lie in an annular region and are enclosed by two rigid cylinders. The viscoelastic liquid is taken in the outer region while viscous fluid lies in the inner region. The analysis was performed by using the potential flow theory for viscoelastic liquid satisfying the Rivlin-Ericksen model. In potential flow theory, the tangential stresses are not considered, the viscosity enters through normal stress balance and the no-slip condition at the two cylindrical rigid boundaries is not enforced. A second-order polynomial in terms of growth rate is achieved and analyzed numerically using the well-known Newton-Raphson method. The results show that the impact of the transfer of heat/mass is found to boost the stability of the interface.