The Senate had accused the SGF of misappropriating funds from non-executed contracts, while EFCC's Magu was indicted by the DSS.
This was disclosed by the President's spokesman, Garba Shehu, in a statement on Sunday, December 18.
"The attention of the presidency has been drawn to a number of reports in the media, in which various accusations of corruption have been levelled against some top officials in the administration," the statement said.
"In that regard, President Buhari has instructed the Attorney General of the Federation to investigate the involvement of any top government officials accused of any wrong-doing. If any of them are liable they will not escape prosecution."
The Secretary to the Government of the Federation, Babachir Lawal, and the Acting Chairman of the Economic and Financial Crimes Commission (EFCC), Ibrahim Magu, have been accused of corrupt practices.
But Shehu's statement did not mention any names.
The Senate had accused Lawal of misappropriating funds from non-executed contracts in the north-east using one of his companies.
Although he denied the allegations, the upper chamber has since demanded his resignation and prosecution.
Similarly, the Senate had on Thursday, December 15, rejected the confirmation of Magu as substantive chairman of the EFCC based on a "security report" purportedly from the Department of State Service (DSS).