Observations of neutral hydrogen (HI) and molecular gas show that 50% of allnearby early-type galaxies (ETGs) contain some cold gas. Molecular gas isalways found in small gas discs in the central region of the galaxy, whileneutral hydrogen is often distributed in a low-column density disc or ringtypically extending well beyond the stellar body. Dust is frequently found inETGs as well. The goal of our study is to understand the link between dust andcold gas in nearby ETGs as a function of HI content. We analyse deep optical$g-r$ images obtained with the MegaCam camera at the Canada-France-HawaiiTelescope for a sample of 21 HI-rich and 41 HI-poor ETGs. We find that allHI-rich galaxies contain dust seen as absorption. Moreover, in 57 percent ofthese HI-rich galaxies, the dust is distributed in a large-scale spiralpattern. Although the dust detection rate is relatively high in the HI-poorgalaxies ($\sim$59 percent), most of these systems exhibit simpler dustmorphologies without any evidence of spiral structures. We find that theHI-rich galaxies possess more complex dust morphology extending to almost twotimes larger radii than HI-poor objects. We measured the dust content of thegalaxies from the optical colour excess and find that HI-rich galaxies containsix times more dust (in mass) than HI-poor ones. In order to maintain the duststructures in the galaxies, continuous gas accretion is needed, and thesubstantial HI gas reservoirs in the outer regions of ETGs can satisfy thisneed for a long time. We find that there is a good correspondence between theobserved masses of the gas and dust, and it is also clear that dust is presentin regions further than 3~Reff. Our findings indicate an essential relationbetween the presence of cold gas and dust in ETGs and offer a way to study theinterstellar medium in more detail than what is possible with HI observations.