Asking to record an interview
There are two points you should touch on:
1. Recording the interview means you will be able to engage in the conversation, rather than being focused on note-taking.
Example: "Would you mind if I record this, so that I may focus on the conversation and not on notes?"
2. You respect their privacy and give them power to opt out.
Example: "If there is anything you would like to say off the record, I can press pause on the recorder. In addition, if at the end of the interview if you have changed your mind, I can delete the audio."
These points remind interviewees that you aren't after confidential or sensitive information and have their best interests in mind.