We develop an analytic theory of the polymer mediated interactions between nanocolloids reversibly adsorbing the excluded volume polymers. This theory describes the limit of the weak adsorption where the correlation length ξ of the polymer system is much smaller than the characteristic adsorption length (colloid absorbance) α. By making use of the developed theory, we calculate the colloid immersion energy and the potential of the polymer mediated interactions as functions of the colloid radius R, the absorbance α, and the polymer volume fraction φ(P).