The dark halo substructures predicted by current cold dark matter simulations may in principle be detectable through strong-lensing image splitting of quasars on small angular scales (0.01 arcseconds or below). Here, we estimate the overall probabilities for lensing by substructures in a host halo closely aligned to the line of sight to a background quasar. Under the assumption that the quasar can be approximated as a point source, the optical depth for strong gravitational lensing by subhalos

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... ypically turns out to be very small (tau < 0.01), contrary to previous claims. We therefore conclude that it is currently not feasible to use this strategy to put the simulation predictions for the dark matter subhalo population to the test. However, if one assumes the source to be spatially extended, as is the case for a quasar observed at radio wavelengths, there is a reasonable probability for witnessing substructure lensing effects even at rather large projected distances from the host galaxy, provided that the angular resolution is sufficient. While multiply-imaged, radio-loud quasars would be the best targets for unambiguously detecting dark matter subhalos, even singly-imaged radio quasars might be useful for setting upper limits on the abundance and central surface mass density of subhalos.