No, you cannot. In the naturalization process, you will have to produce a current, valid passport. It will also be much easier for you if you have a current green card - or a*very * good reason why you do not So, my advice is to get a new passport from your country's consulate, and a new green card from USCIS.
It would be best for you to apply for a green card extension first before applying for citizenship as the USCIS may require you to have a valid green card at the time of applying for citizenship.
In order to apply for naturalization, the regulations require you to have a permanent resident card that is valid for at least 6 months. Thus, you must renew your green card before you can apply to become a naturalized citizen. The application is filed on form I-90.
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