Abati was arrested last Monday for allegedly benefiting from the controversial $2.1bn allegedly diverted by Dasuki.
According to Leadership newspaper, which quoted a family source, the EFCC refused to release Abati without giving any explanations.
"We don’t know why they are still keeping our brother despite him meeting the bail condition of EFCC. Nigerians can now see that it is not about fighting corruption but going after perceived political enemies and critics of the government," the source was quoted as saying.
The anti-graft agency had granted Abati administrative bail on October 27.
As part of his bail conditions, he was required to submit his International Passport and produce a surety who is a Level 16 civil servant.
He was arrested on Monday, October 24 for allegedly collecting N50 million from the detained former National Security Adviser (NSA), Sambo Dasuki.
The money is believed to be part of the controversial $2.1 billion allegedly diverted by the ex-NSA.