Pressure is mounting after the expiration on Thursday of a three-month constitutional deadline after parliament's rejection of Ahmadinejad's first candidate for the job on 24 August.
"I do not believe in extension of the three-month deadline, and nomination of an oil minister should be done within a minimum of time," Guardians Council spokesman Abbasali Kadkhodai said on Saturday, according to the student news agency ISNA.
Ahmadinejad, whose country is the second-biggest Opec producer, was forced last week to retain Kazem Vaziri-Hamaneh as interim caretaker of the Oil Ministry after parliament said his third choice, Seyed Mohsen Tasaloti, was unqualified.
The constitution does not say what happens if no candidate is confirmed by the parliament within the three-month timeframe.
"There is no ambiguity in the existing law and if the official commitment is not fulfilled under the deadline, then it should be carried out within the least time," said the spokesman for the Guardians Council.
The 12-member body has the authority to interpret the constitution and determine whether laws passed by the parliament are in line with the constitution and Islamic law.
Tasaloti was said to be a millionaire whose family spends most of its time abroad and was rejected for lack of expertise.
The two previous nominees had also been shunned over their lack of experience in the oil sector, which accounts for 80% of Iran's foreign exchange income.