The appeal was first created on the presidential website on September 1. According to the website, the president of Ukraine may submit the petition for consideration to lawmakers he deems it appropriate.
Saakashvili, who is wanted in Georgia on charges of misappropriation of public funds and abuse of power, said earlier that he did not see himself becoming the head of the Ukrainian cabinet.
The Ukrainian leadership suggested that a cabinet reshuffle would take place this fall.
Saakashvili’s 2004-2013 rule as leader of the former Soviet republic of Georgia was criticized as authoritarian. Saakashvili has lived in Europe and the United States since 2013 and has yet to return to his homeland.
Poroshenko granted Saakashvili Ukrainian citizenship and appointed him the governor of Odessa in May of this year.