In this article, we prove the proximinality of closed unit ball of M-ideals of compact operators on Banach spaces. We show that every positive (self-adjoint) operator on a Hilbert space has a positive (self-adjoint) compact approximant from the closed unit ball of space of compact operators. We also show that K(L1), the space of compact operators on L1, is ball proximinal in B(L1), the space of bounded operators on L1, even though K(L1) is not an M-ideal in B(L1). Moreover, we prove the ball proximinality of M-embedded spaces in their biduals. © 2021 American Mathematical Society. All rights reserved.