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.