Form I-131 should be filed for advance parole.

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Generally, if you are seeking immigrant status like a green card, it is important to have all the documents in order, especially if you are going to travel abroad, before getting the green card on hand. If that is the case, one has to apply for a reentry permit, refugee travel document or advance parole travel document. If the application for advance parole is accepted, you may be able to travel and enter the U.S.
If you want to renew your advance parole document I-512L or I-512, the USCIS will accept the Form I-131 filed up to 120 days before the date of your current Advance Parole document expires. Some applicants who have filed or will file Form I-485 for registering permanent residence or adjustment of status. The advance parole card can be obtained by filing form I-131 and I-765 together.Those who already filed form I-485 which is pending must use form I-765 and use the location instructions for form I-485.