It is best to follow the instructions that accompany the form.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.
DO NOT DO IT. You must be in the US to file. See "Who may file" part 1A: http://www.uscis.gov/files/form/i-131instr.pdf
FORMER IMMIGRATION LAW PROFESSOR -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.
You must be physically present in the United States when you file for a re-entry permit. You will be required to go to a biometrics appointment in the United States on a scheduled appointment date.
I strongly recommend an appointment or teleconference with a competent and experienced immigration attorney to discuss your options.
This is general information, not legal advice, and does not create an attorney client relationship.
Doing this will put you at risk of a finding of fraud either now or in the future as essentially you are saying you are within the US, when your passport stamps and your record at the border will show that you are not.
more fundamentally how you should proceed depends on if you are planning to apply for citizenship or want to preserve residency for your green card only.
if you want citizenship, do not stay out of the country for over a year continuously.
Dhenu Savla, Esq
As others have said, you should not file the I-131 while you are physically outside the U.S. Also of concern is whether you have adequately maintained your permanent intent in order to keep your permanent resident status. I would strongly recommend talking to an experienced immigration attorney as soon as possible and certainly before filing any paperwork or attempting to enter the U.S.