On Saturday, the president of Ukraine Petro Poroshenko admitted Saakashvili to Ukrainian citizenship, and also signed a decree appointing him the governor of Odessa and presented to the city's officials.
Under the Georgian law about dual citizenship, Saakashvili should apply to the president in order to receive dual nationality.
"This is the law adopted by Saakashvili himself. If he becomes the governor and receives Ukrainian citizenship, he loses his Georgian citizenship."
According to the deputy, "if the Georgian government decides to grant the former president dual citizenship, it would be an irresponsible decision."
Saakashvili has been a fugitive from justice in Georgia since 2013, after Georgian prosecutors charged him with numerous offences, from abuse of power to misappropriation of funds to over $5 million in embezzlement charges.
Georgia has repeatedly asked Ukraine to extradite Saakashvili, who was appointed as an advisor to the Ukrainian government earlier this year. The country has also tried, unsuccessfully, to get the ex-president on Interpol's wanted list.