Even though the green is expired you still remain a permanent resident. However, there are times when a green card may be requested for so it is best that you have it renewed. Nevertheless, there are no laws that bound you to renew the expired card before applying for your citizenship.
To tell you the truth, in most cases USCIS would like you to have the green card valid however they are not entitled to reject the Form N-400 basing on an expired card. It should be pointed out that the situation with a conditional green card is entirely different. In case the card was granted to you because of marriage to a US citizen, you are bound to renew it 90 days prior to its 2-year expiration date. If you fail to do so your conditional resident status will expire and you may end up getting deported in the end. That is why it is best if you apply for the renewal together with your spouse three months before the expiration to avoid any misunderstanding. Form I-751 is the one you need to succeed with the process.
As it has been mentioned, the USCIS is not able to force you to renew the card after the expiration although it is preferable if it is still valid when you are about to apply for naturalization. Besides, it is advantageous to you to have a valid card since with it expired loans, traveling, employment, and other things may be hard to achieve.
To sum everything up, it is safe to say if you really want to get a US citizenship without any implications it is best that you file for it before your green card expires.
March 3, 2020