HESS J1825–137 is a bright very high-energy gamma-ray source that has been firmly established as a pulsar wind nebula (PWN), and one of the most extended gamma-ray objects within this category. The progenitor supernova remnant (SNR) for this PWN has not been firmly established. We carried out an analysis of gamma-ray observations in the region of HESS J1825–137 with the Fermi–LAT that reveals emission in the direction away from the Galactic plane. The region lies beyond the PWN and reaches a distance from the pulsar compatible with the supposed location of the SNR shock front. The spectrum of the gamma-rays is hard with a photon index of ∼1.9 in the 10–250 GeV range. Several scenarios for the origin of the emission are discussed, including the SNR as a source of high-energy particles and the ‘leakage’ of leptons from the PWN.