Interesting question. The best would probably to first identify the characteristics of owl’s hearing (some reading required, such as here) and then determine what kind of equipment would work best to reproduce it.
Of course, this will be more than just signal input (the sounds going into one or more microphones, most likely an array of them), but also signal processing and analysis to give meaning to the sounds.
Furthermore, this analysis would most likely require moving the input array’s direction to further target the sound of interest.
Maybe looking at what kind of equipment is used to record (specific) nature sounds could help, such as this article.
All in all, this sounds like a complex project. Keep us updated on your progress as this is certainly an interesting idea.