The JAXA/ISAS spacecraft DESTINY + will be launched to the active asteroid (3200) Phaethon in 2022. Among the proposed core payload is the DESTINY + Dust Analyzer (DDA) which is an upgrade of the Cosmic Dust Analyzer flown on the Cassini spacecraft to Saturn (Srama et al., 2011). We use two up-to-date computer models, the ESA Interplanetary Meteoroid Engineering Model (IMEM, Dikarev et al., 2005a,c), and the interstellar dust module of the Interplanetary Meteoroid environment for EXploration model (IMEX; Sterken et al., 2013;Strub et al., 2019) to study the detection conditions and fluences of interplanetary and interstellar dust with DDA. Our results show that a statistically significant number of interplanetary and interstellar dust particles will be detectable with DDA during the 4-years interplanetary cruise of DESTINY + . The particle impact direction and speed can be used to descriminate between interstellar and interplanetary particles and likely also to distinguish between cometary and asteroidal particles.