Mr. Abati was detained when he reported at the EFCC headquarters a week ago.
During the interrogation, he reportedly admitted receiving N50 million from a former National Security Adviser, Sambo Dasuki.
The government said the money was part of $2.1 billion earmarked for the purchase of arms for the fight against Boko Haram.
Mr. Dasuki is standing trial for allegedly misappropriating the money.
Sources at the anti-graft agency told newsmen on Monday night that Mr. Abati offered to refund N5 million to the government.
The source said Mr. Abati allegedly failed to furnish the EFCC with records of how the N50 million was disbursed.
The former spokesperson reportedly said he did not keep notes of such expenses as they were doled out to media practitioners across the country as part of the 2015 campaign activities.
Mr. Abati may still be allowed to go home if he is able to meet an administrative bail granted to him last week.
He had not been able to meet the bail requirements, which included presenting a senior federal civil servant —from the level of a director— as surety.
“He may be released in the coming days despite his refusal to fully cooperate with us,” one EFCC source said.
On Monday, Mr. Abati, alongside a former Minister of Aviation, Femi Fani-Kayode, and Musiliu Obanikoro, were visited in custody by a Catholic cleric, Matthew Kukah.
Mr. Obanikoro has been in EFCC custody since he turned himself in hours after returning to the country on October 17.
Mr. Fani-Kayode was rearrested outside a Lagos court on October 21.
A statement by the EFCC said Mr. Kukah commended the agency for taking a good care of the detainees.