Aims. We aim to investigate the dynamical fate of meteoroids ejected during past perihelion passages of comet 45P/Honda-Mrkos-Pajdusakova that intersect the orbit of Venus. Of particular interest is the possibility, borne of previous work, that a significant flux of these particles will reach the planet during early June and late August 2006, when the Venus Express spacecraft will be operating in orbit around Venus. Methods. We have simulated the generation of meteoroid trails ejected by the comet at some past perihelion passages, and numericaly integrated them forward in time until they approach Venus in 2006. Results. On the inbound leg of the comet's path towards perihelion, we find a trail composed of dust particles ejected between 1943 and 1980 that encounters Venus on 9 June 2006 at a distance of 0.009 AU. On the outbound leg, we observe a dense trail of particles ejected between 1985 and 2001 that measures 3.4 × 10−4 AU (5 × 104 km) in half-width, and passes under the planet at a distance of 1.72 × 10−3 AU (2.6 × 105 km) on 30 August. Based on these results, we conclude that, on both occasions, the incident flux at Venus will likely be too low to allow for the detection of a shower by optical means. We discuss the circumstances under which Venus Express may encounter a significant flux of small particles detectable through impact ionization or disturbances in the interplanetary magnetic field.