Context. Molecular clouds are predicted to emit nonthermal X-rays when they are close to particle-accelerating supernova remnants (SNRs), and the hard X-ray source AX J1714.1−3912, near the SNR RX J1713.7−3946, has long been considered a candidate for diffuse nonthermal emission associated with cosmic rays diffusing from the remnant to a closeby molecular cloud. Aim. We aim at ascertaining the nature of this source by analyzing two dedicated X-ray observations performed with Suzaku and Chandra. Methods. We extracted images from the data in various energy bands, spectra, and light curves and studied the long-term evolution of the X-ray emission on the basis of the ~4.5 yr time separation between the two observations. Results. We found that there is no diffuse emission associated with AX J1714.1−3912, which is instead the point-like source CXOU J171343.9−391205. We discovered rapid time variability (timescale ~ 10³ s), together with a high intrinsic absorption and a hard nonthermal spectrum (power law with photon index Γ ~ 1.4). We also found that the X-ray flux of the source drops down by 1–2 orders of magnitude on a timescale of a few years. Conclusions. Our results suggest a possible association between AX J1714.1−3912 and a previously unknown supergiant fast X-ray transient, although further follow-up observations are necessary to prove this association definitively.