Magnetic Resonance Imaging (MRI) is one of the most powerful diagnostic tools providing maps of 1H relaxation times of human bodies. The method needs, however, a contrast mechanism to enlarge the difference in the relaxation times between healthy and pathological tissues. In this work, we discuss the potential of a novel contrast mechanism for MRI based on Quadrupole Relaxation Enhancement (QRE) and estimate the achievable value of QRE under the most favorable conditions. It has turned out that the theoretically possible enhancement factors are smaller than those of typical paramagnetic contrast agents, but in turn, the field-selectivity of QRE-based agents makes them extremely sensitive to subtle changes of the electric field gradient in the tissue. So far, QRE has been observed for solids (in most cases for 14N) as a result of very slow dynamics and anisotropic spin interactions, believed to be necessary for QRE to appear. We show the first evidence that QRE can be achieved in solutions of compounds containing a high spin nucleus (209Bi) as the quadrupole element. The finding of QRE in a liquid state is explained in terms of spin relaxation theory based on the stochastic Liouville equation. The results confirm the relaxation theory and motivate further exploration of the potential of QRE for MRI.