This paper reports the search for quiescent low-mass X-ray binaries (qLMXBs) in the globular cluster (GC) NGC 6553 using an XMM-Newton observation designed specifically for that purpose. We spectrally identify one candidate qLMXB in the core of the cluster, based on the consistency of the spectrum with a neutron star H-atmosphere model at the distance of NGC 6553. Specifically, the best-fit radius found using the three XMM European Photon Imaging Camera spectra is R_NS=6.3(+2.3)(-0.8) km (for M_NS=1.4 Msun) and the best-fit temperature is kTeff=136 (+21)(-34) eV. Both physical parameters are in accordance with typical values of previously identified qLMXBs in GC and in the field, i.e., R_NS~5-20 km and kTeff~50-150 eV. A power-law (PL) component with a photon index Gamma=2.1(+0.5)(-0.8) is also required for the spectral fit and contributes to ~33% of the total flux of the X-ray source. A detailed analysis supports the hypothesis that the PL component originates from nearby sources in the core, unresolved with XMM. The analysis of an archived Chandra observation provides marginal additional support to the stated hypothesis. Finally, a catalog of all the sources detected within the XMM field of view is presented here.