Waleed al-Tabtabai, Mohammed al-Mutair and Mohammed Hayef, all Sunni Muslim Salafi MPs, said in a joint statement that they will file the request on Monday.
Shiite cleric Mohammad Baqer al-Fali arrived in Kuwait from Tehran on Thursday and was detained briefly before he was released and allowed to stay in the country.
The MPs say Fali is banned from entering the Gulf emirate after a Kuwait court convicted him of insulting some of the Prophet Mohammed's companions who are revered by Sunni Muslims but not by Shiites.
The cleric was fined 10,000 dinars (37,000 dollars) by a lower court in June. The appeals court is due to rule on the case next month.
The three MPs hold Prime Minister Sheikh Nasser Mohammed al-Ahmad al-Sabah responsible for breaching Kuwaiti law by allowing a person to enter the country despite a ban against him.
But a Kuwaiti interior ministry spokesman, Mohammed al-Sabr, later said that the Iranian cleric was expected to leave the emirate on Thursday at the latest.
Fali is "undesirable" in Kuwait — where he has a valid residency permit until 2011 — but was granted, at his request, "a deadline until Thursday" to leave.
The deadline was given to allow the cleric to take care of personal business in Kuwait, the spokesman said.
Three weeks ago, a liberal-leaning MP threatened to grill the prime minister, a nephew of the ruler, over his management of the economic crisis and claims of misappropriation of funds.
He has however suspended his threat for three months.
The only time a request was filed to grill the prime minister was in March 2006, resulting in the emir dissolving parliament and calling for fresh elections.
