How can I update the lead source for converted leads (contact)?

I am looking at the Analytics-Sales Funnel, and I can see that there are leads converted to contacts that do not have a source lead. I am trying to correct them so we can use properly track (btw, we just standardized our lead source so the data is messy). I tried updating the lead source manually in the contact modules, however, it does not reflect on the reports. 

Is this possible? Thank you!