Osinbajo, a Professor of Law and Senior Advocate of Nigeria, made this known while speaking with journalists at the Presidential Villa.
He added that the Presidency is fully in support of Magu emerging as the substantive chairman of the EFCC.
He said: “It is up to the Senate to make their judgement and it is up to us say what we want to do.
“If our candidate is rejected, we can re-present him.
“No law says we can't re-present him.
“And again, there is the other argument, whether or not we need to present him for confirmation and that's a compelling argument from Femi Falana.
“His argument is that under the constitution, section 171, and if you look at that section, it talks about the appointments that the president can make.
“They include appointments of ministers, ambassadors and heads of agencies such as the EFCC.
“In that same section 171, the constitution rightly said that certain appointments must go to the Senate such as ministerial and ambassadorial appointments.
“Those of heads of agencies like the EFCC do not have to go to the Senate.
“That's what the constitution says.
“But the EFCC Act, which of course as you know is inferior, says that EFCC chairman should go to the Senate for confirmation.
“I am sure that even a pocket book lawyer knows that when a legislation conflicts with constitution, it's the constitution that prevails.
“I agree with Mr. Falana that there was no need in the first place to have sent Magu's name to the Senate, but we did so and it was rejected by the Senate, but I believe that it can be re-presented.
“I don't think there is anything wrong about the fact that Senate has rejected him.
“Senate has acted in its own wisdom to say 'no, we don't want him', and we can say 'this is our candidate… we like the gentleman and we want him to continue.'”
Speaking on report of the Department of State Services that indicted Magu, Osinbajo said President Muhammad Buhari could have interfered with the DSS report if he wanted to, but that he decided to hear Magu's own account, after which he felt convinced to retain the anti-graft czar.
Osinbajo said: “We should commend the President for not interfering with what the DSS said.
“The DSS came up with a report and the man who was accused refuted it.
“He explained and gave a reason.
“When that happened, the President looked at what Magu said and what the DSS wrote and he said: 'I am satisfied with what Magu said.'
“He then decided to retain Magu as the nominee for EFCC.
“I don't see any reason why that should be contested.
“The President has not interfered with what the DSS said.
“If he wanted to interfere, he would have ordered the DSS to keep quiet.
“He didn't do that, but he said: 'I don't think the DSS report is meritorious enough to withdraw his nomination.'
“The President reserves the right to say: 'this is who I want.'
“I'm fully in support of Magu as the EFCC chairman just as the President is.”
It could be recalled two weeks ago, the Senate stopped the confirmation of Resident Electoral Commissioners of the Independent National Electoral Commission in protest of the decision of the executive to retain Magu as the head of the EFCC