If the substantive part of a story comes from the mouth of the person saying it, as in quotes and videos, and I trust that that hasn't been faked or misrepresented (which is easy if the story IS the quote), I don't care what the source is.  Looks like I gave the link to a list of stories that have changed, so it's not working now.  Sorry about that.

It's covered by a bunch of sources, including Fox News, which may have broken it (I haven't dug into it).  Pick your own if you wish from an internet search with your preferred search engine.  It's a fact that Giuliani is telling this story about Trump going to him seeking advice about banning Muslims to the media.

Here's one link:

https://www.washingtonpost.com/news/the-fix/wp/2017/01/29/trump-asked-for-a-muslim-ban-giuliani-says-and-ordered-a-commission-to-do-it-legally/?utm_term=.e81b0258072d