No. You have to apply with a valid passport.

Note that there are exception: If you are a permanent resident of the U.S. (Green Card holder) and cannot get a passport from your home country because it does not issue passports to permanent residents of other countries, you can apply with:

your U.S. Refugee Travel Document (I-571), 


your Permit to Re-enter the United States (I-327).

Enter the document number in the passport number field  when applying.