The High-Energy Storage Ring (HESR) is part of the upcoming International Facility for Antiproton and Ion Research (FAIR) at GSI in Darmstadt. The HESR is planned to dedicate to the field of high-energy antiproton physics to explore the resear ch areas of charmonium spectroscopy, hadronic structure, and quark-gluon dynamics with high-quality beams over a broad momentum range from 1.5 to 15 GeV/c. The new facility provides the combination of powerful phase-space cooled antiproton beams and inter nal Pellet and gas jet targets to achieve the requirements of the experiment PANDA in terms of beam quality and luminosity. Detailed theoretical analyses have been carried out to design the stochastic cooling system for accumulation and stochastic cooling of antiprotons with target operation. Recently it is proposed to utilize the HESR also for the atomic and nuclear physics with highly charged heavy ions such as 132Sn50+ in the dedicated experiments at high energies 0.74-3 GeV/u. In this contribution the feasibility of stochastic cooling of heavy ions with internal targets is in detail investigated under the constraint of the cooling system hardware as foreseen for anti-proton cooling.