The upper chamber said the only condition to reconsider Magu is if the President provides convincing explanations to do so.
The upper chamber said it may reconsider Magu if President Muhammadu Buhari provides the necessary explanation for it to do so.
On Thursday, December 15, the lawmakers rejected Magu's nomination based on a "security report" on him by the Department of State Services (DSS).
In the report, the Acting EFCC Chairman was said to have been accused of various corruption-related offences.
The Chairman, Senate Committee on Media and Public Affairs, Senator Sabi Abdullahi, said the chamber has taken its decision and it is left for Buhari to take the next step.
"This is not an issue that is ambiguous and I will not take issue with anybody. What we have said is very straightforward and unambiguous. It is not our responsibility or in our power to tell Mr. President what to do," he told the newspaper on Friday, December 16.
"It is his prerogative and for every action taken, there must be a basis. Let him take any action but, of course, he will base his action on explanations. If that happens, we will take his explanations based on their face value and see. Until then, our decision is very simple. It is unambiguous; that is what we said from the beginning and that is what we stand by," he said.
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Meanwhile, according to the Chairman, Senate Committee on Media and Public Affairs, Magu's rejection will be formally communicated to the Presidency by next week.