I was curious too. My weak Google-fu didn't come up with anything from the FSF, but the GNU project has a page[0] explaining that they don't endorse Manjaro because it "includes nonfree software through its normal channels", "ships nonfree blobs with its kernel", and "includes a proprietary office suite and proprietary games with DRM."

[0]: https://www.gnu.org/distros/common-distros.en.html

I can't find anything. FSF's site doesn't seem to even mention Manjaro. The only thing I could find that references both the FSF and Manjaro is this article from GNU explaining why they don't endorse any particular distribution:

https://www.gnu.org/distros/common-distros.en.html

Plus as mentioned in the article Manjaro includes non-free software so I doubt GNU/FSF would recommend it even if they did endorse certain distributions.

The author has updated the article to name Parabola as the distribution preferred by the FSF.