In-situ production of long-lived isotopes by cosmic muon interactions may generate a non-negligible background for deep underground rare event searches. The underground production of 77(m)Ge through fast neutron capture on 76Ge has been identified as the main in-situ cosmogenic background [1] in the future ton-scale experiment LEGEND-1000 [2] searching for 0νββ of 76Ge. Siting the experiment at Gran Sasso National Laboratory (LNGS) results in a higher production of 77(m)Ge with respect to SNOLAB (baseline site for the experiment) because of the reduced rock overburden. Therefore suppression methods have been proposed to tag and discriminate 77(m)Ge background events [3]. Here we present a technique that further reduces the 77(m)Ge production rate. Fast neutrons produced in the liquid argon are slowed down using hydrogen-containing neutron moderators. Neutrons are then more likely to be captured in argon than in germanium, decreasing the 77(m)Ge production rate. In this poster, Monte Carlo simulations are presented to optimize the neutron moderator design while keeping the background index unaffected due to the intrinsic radioactivity of the moderator material. [1] Monte Carlo evaluation of the muon-induced background in the GERDA double beta decay experiment, L. Pandola, M. Bauer, K. Kröninger, X. Liu, C. Tomei, S. Belogurov, D.Franco, A. Klimenko, M. Knap, Nucl. Instr. Methods A 570 (2007) 149 [2] LEGEND-1000 Preconceptual Design Report, LEGEND Collaboration, N. Abgrall et al.,arXiv:2107.11462 [physics.ins-det] [3] Virtual depth by active background suppression: revisiting the cosmic muon induced background of GERDA Phase II, C. Wiesinger, L. Pandola, S. Schönert, Eur. Phys. J. C(2018) 78:597