We study the stable unextendibility of vector bundles over the quaternionic projective space HP^n by making use of combinatorial properties of the Stiefel-Whitney classes and the Pontrjagin classes. First, we show that the tangent bundle of HP^n is not stably extendible to HP^<n+1> for n ≥ 2, and also induce such a result for the normal bundle associated to an immersion of HP^n into R^<4n+k>. Secondly, we show a sufficient condition for a quaternionic r-dimensional vector bundle over HP^n not to be stably extendible to HP^<n+l> for r ≤ n and l > 0, which is also a necessary condition when r = n and l = 1.