Melaye said there is a provision of the Senate rules which would not allow members consider Magu for the same position again.
The Senate last week failed to confirm Magu as the substantive chairman of the anti-graft agency, making it the second the lawmakers would reject him.
Melaye, who is the Chairman, Senate Committee on Federal Capital Territory (FCT), said there is a provision of the Senate rules which would not allow members consider Magu for the same position again.
As contained in a statement signed by Melaye, the lawmaker disclosed this while commenting on the debate in the media about whether Buhari can renominate Magu for the third time.
According to Order 131 of the Senate Rules, Melaye said after the rejection of Magu's nomination, his candidacy is considered lapse and therefore advised the President to consider a fresh nominee who is qualified, in terms of experience, integrity, knowledge and temperament to lead the anti-graft agency.
Order 131 of the Senate Rules states that "nominations neither confirmed nor rejected during the session or within 21 working days in the case of Ministerial nominees shall be returned by the clerk to the National Assembly to the President of the Federal Republic of Nigeria and shall not again be made to the Senate by the President of the Federal Republic of Nigeria."
During the last hearing on Magu's confirmation, Melaye said the Acting EFCC Chairman even failed to impress some senators who would hav supported him.
He said: "Those suggesting to the President that after failing to scale the confirmation process twice, the President should leave Magu to be acting are only recommending violation of the law, disrespect for due process and perpetration of illegality. All these will only undermine democracy and constitutionalism in our country.
"Those drafters of the law who made the provision that the Senate should confirm the nomination of the EFCC chairman did not make any mistake and nobody should observe the law in the breach by getting a person into that office who has not been confirmed. Magu is not greater than the law creating EFCC. Magu is not the last messiah. He can't be the only competent person for the job out of 170 million Nigerians. Should he voluntarily decline the appointment today, will EFCC fold up?"
Following his second rejection, Magu had said that the Senate's decision would not deter him from fighting corruption with all his might as the Acting EFCC boss.