From what I can see:
- http://visa.ywpw.com/ChineseVisa/nonUSCitizen_en.html (mirror) and Wikipedia do not mention it
- https://www.saporedicina.com/english/chinese-visa-application/(mirror) says it's possible: "U.S. citizens may be eligible for a 10-year multiple entry Visa. [...] You can apply for this visa even if you don’t have an American passport but are still a resident of the United States."
- http://www.chinaconsulatesf.org/eng/lszj/zgqz/t751633.htm (mirror): "U.S. permanent resident card holders who have lived overseas for at least one year can apply for a multiple-entry permit valid for 2 years." but I'm not sure what they mean by overseas, that could be living in Hong Kong given the context.
So it's quite unclear to me what the answer is.
I am interested in the case of French citizens if that matters. French citizens may only apply to a one-entry or two-entry Chinese L (tourist) visa (up to 30 days per entry), unless perhaps if they are lawful permanent residents in the United States.