You do not need a foreign passport to apply for US citizenship. You will, however, need a copy of your legal permanent resident card to show your eligibility to apply for citizenship. With that said, it is always a good idea to have a foreign passport and/or a copy of a birth certificate when dealing with immigration matters.
Having a foreign passport is not a requirement for naturalization.
The link takes you to the USCIS website with information on Naturalization requirements.
Technically, you don't have to have it. However, Form N-400 asks questions about every trip that you made outside the US during the preceding 5 years, dates and locations. Your passport is usually the best way to obtain this information.