The anti-graft agency said the ex-minister collected N785million from ONSA while in office.
His family and some close friends and associates are understood to be rallying around him to raise the funds as a first step to secure his bail.
From ONSA, about N4.685billon was transferred to Sylva McNamara Limited, a company allegedly linked to Obanikoro.
The ex-Minister told EFCC interrogators that N3.880billion of the N4.685billion was allocated to Governor Ayo Fayose of Ekiti State and Senator Iyiola Omisore.
He said he handed over $5.377million (about N60 million then) to Fayose at Spotless Hotel, Ado-Ekiti in the presence of the former Secretary of the Peoples Democratic Party in the state, Dr. Tope Aluko and other party stalwarts.
He also claimed the balance of N785million was expended on alleged anti-Boko Haram campaign in Lagos and the South-West.
A source, who spoke in confidence, told The Nation that, “The ex-minister has been cooperating with detectives and he appears willing to refund some cash out of the N785m traced to Sylvan McNamara.
“I think his associates and friends have rallied around him, having discovered that the bulk of the cash from ONSA went to Fayose and Omisore.
“I think he might initially refund N100 million to get bail reprieve in order to prevail on others who benefited from the N785million to repay the slush funds.
“The refund is one of the issues delaying the granting of bail to the ex-minister.”