Observations of δ Ori A made with the UHRF in its highest resolution mode (R≈900 000) have revealed the presence of a cool (Tk⩽350 K) variable absorption component at a heliocentric velocity of +21.3 km s−1. The component is detected in Na I D1, where clear hyperfine splitting is seen, and Ca II K. Comparison of our data with existing spectra suggests that the component has consistently increased in strength from 1966 to 1994, and subsequently reduced in intensity by 1999. Following a discussion of the possible origins of this component it is concluded that an interstellar, rather than circumstellar, origin is most likely. This is one of very few detections of variable interstellar absorption reported in the literature, and we suggest an origin within filamentary material associated with the expanding H I shell surrounding the Orion-Eridanus superbubble