Well, one doesn't really "make" an interview, of course. "Conduct," barring meanings related to music, either means:
1) "To comport (oneself) in a specified way." Like:
"The lie was obvious from the way he conducted himself."
Or,
2) "To direct the course of; manage or control."
The latter is what is meant here, of course: we decided to manage/lead/control the interview; ergo, conduct it.