The EFCC is said to be dissatisfied with Obanikoro's claim that he spent N785m on anti-Boko Haram campaign souvenirs.
According to Punch, the Economic and Financial Crimes Commission (EFCC) might release Obanikoro this week on administrative bail of N100 million.
The former minister surrendered himself to the EFCC last Monday upon arriving the country from the United States, and he has been detained and interrogated since then.
The anti-graft agency said it traced N4.7 billion to a company, Silva Mcnanamara, in which Obanikoro has interests.
Two of the former minister's sons, Babajide and Gbolahan, were said to be directors of the company when the money was allegedly paid into the company’s accounts from the office of the National Security Adviser in 2014.
The money was largely believed to have been used in funding the June 21, 2014 Ekiti State governorship election, which Governor Ayodele Fayose won, and the November 2014 governorship poll in Osun State, which Chief Iyiola Omisore of the Peoples Democratic Party contested and lost.
"We are concerned about his health and we are not ready to see him still in detention beyond Tuesday this week. The man’s life is more important than the money they are asking him questions about," a family source told the newspaper.
"If that is the only condition (N100m) to see him out of detention, for now, we are making efforts to raise that. You know the situation of the country now, but no sacrifice is too much to make him a free man again," the source added.
Report said EFCC investigators are not satisfied with Obanikoro's explanation on how N785 million was spent - the money he said was spent on souvenirs to promote a campaign against the Boko Haram in Lagos.
He also reportedly said N200 million was spent on surveillance activities while another N200 million and the balance of N385 million were spent on logistics and operations under the supervision of the owner of McNamara, who he identified as Taiwo Kareem.