We present the results of a targeted search for intervening H i absorption in six nearby, gas-rich galaxies using the Australia Telescope Compact Array. The sightlines searched have impact parameters of 10–20 kpc. By targeting nearby galaxies, we are also able to map their H i emission, allowing us to directly relate the absorption-line detection rate to the extended H i distribution. The continuum sightlines intersect the H i disc in four of the six galaxies, but no intervening absorption was detected. Of these four galaxies, we find that three of the non-detections are the result of the background source being too faint. In the fourth case, we find that the ratio of the spin temperature to the covering factor (T S/f) must be much higher than expected (≳5700 K) in order to explain the non-detection. We discuss how the structure of the background continuum sources may have affected the detection rate of H i absorption in our sample, and the possible implications for future surveys. Future work including an expanded sample, and very long baseline interferometry observations, would allow us to better investigate the expected detection rate, and influence of background source structure, on the results of future surveys.