Form referrer field not working with API v2?

On each subscriber's profile, under tab "Other", there is a field called "referrer", which states which form was used to subscribe.
With out of the box integration of the minimal form, my tests show "minimal" as the referrer, which is correct.
Although it is not documented in the Custom coded forms documentation page, i understand the referrer is passed via the following hidden form <input type="hidden" name="nr" value="minimal">.

Now, my project involves sending the miniaml form via TNP's API v2 to "subscriptions" endpoint.
Fieldname "ne" as stated in the same documentation page would return an error via the API. To make it work I had to change the email input field's name attribute with name="email", thus matching parameters indicated in API v2 reference page.
However, the form referrer is not passed for subscribers registering this way, and API v2 reference page, does not seem to include any form referrer field.
Is is currently possible to pass the form referrer field via API ? If so how should I name the field?