Should I follow up after interview?

I had a 2nd (final) interview at a company. The hiring manager emailed me the next day and said "We're reviewing other candidates, but HR should be getting in touch with you to ask for your references. If you don't hear back in a couple days, let me know." It's been a week and HR never contacted me. Now here's the thing, I haven't followed up either, BECAUSE I'm very hesitant to give out my references if an offer isn't imminent. I'm currently already employed and this whole job interview was done in secret. I don't want my references to know I'm looking for a job unless I need to. Should I follow up with the hiring manager and risk having to give my references out?

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