Recently, a theoretical study [Z.-X. Li , npj Quantum Mater. 6, 36 (2021)2397-464810.1038/s41535-021-00335-4] investigated a model of a disordered d-wave superconductor, and reported local time-reversal symmetry breaking current loops for sufficiently high disorder levels. Since the pure d-wave superconducting state does not break time-reversal symmetry, it is surprising that such persistent currents arise purely from nonmagnetic disorder. Here, we perform a detailed theoretical investigation of such disorder-induced orbital currents, and show that the occurrence of the currents can be traced to the emergence of local (extended) s-wave order coexisting with underlying disordered d-wave pairing, making it favorable to generate local s±id regions. We discuss the energetics leading to such regions of s±id order, which support spontaneous local current loops in the presence of inhomogeneous density modulations.