Define a quasi-amicable pair as a pair of distinct natural numbers each of which is the sum of the nontrivial divisors of the other, e.g., {48, 75}. Here nontrivial excludes both 1 and the number itself. Quasi-amicable pairs have been studied (primarily empirically) by Garcia, Beck and Najar, Lal and Forbes, and Hagis and Lord. We prove that the set of n belonging to a quasi-amicable pair has asymptotic density zero.