He arrived at Livingston police station for talks on Tuesday, saying he did not know why he was there.
BBC Scotland understands a former administrator, David Whitehouse, has also been detained.
Mr Green took control at rangers after buying the club's assets following administration and liquidation in 2012.
He stepped down following allegations that he was working in conjunction with the club's former owner Craig Whyte.
David Whitehouse, who worked for Duff and Phelps when the club went into administration, has also previously been arrested and charged.
It is unclear what charges Mr Green is facing, but he has already spoken to the police on three occasions.
Arriving at the police station on Tuesday morning, he said: "I've been invited to attend an interview with Police Scotland. I have done that on a number of occasions in the past."
Asked why he was there, Mr Green replied: "Well, one of the difficulties with today is my legal people had asked Police Scotland to provide us information that we're likely to be questioned on and they wouldn't provide that so I'm at a loss really."