Primordial black holes, allegedly formed in the very early Universe, have been proposed as a possible viable dark matter candidate. In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation space-borne interferometer μAres arising from a population of primordial black holes orbiting Sgr A, the supermassive black hole at the Galactic Center. Assuming that such objects indeed form the entire diffuse mass allowed by the observed orbits of stars in the Galactic Center (4×103 M within a radius of 10-3 pc from Sgr A), under the simplified assumption of circular orbits and monochromatic mass function, we assess the expected signal in gravitational waves, either from resolved and nonresolved sources. We estimate a small but non negligible chance of 10% of detecting one single 1 M primordial black hole with LISA in a 10-year-long data stream, while the background signal due to unresolved sources would essentially elude any reasonable chance of detection. On the contrary, μAres, with a 3 orders-of-magnitude better sensitivity at 10-5 Hz, would be able to resolve 140 solar mass primordial black holes in the same amount of time, while the unresolved background should be observable with an integrated signal-To-noise ratio 100. Allowing the typical PBH mass to be in the range 0.01-10 M would increase LISA chance of detection to 40% towards the lower limit of the mass spectrum. In the case of μAres, instead, we find a "sweet spot"just about 1 M, a mass for which the number of resolvable events is indeed maximized.
