Kevin McGeever, 68, was arrested at his home in County Galway, the Belfast Telegraph reported Friday.
McGeever was being held under a section of the penal code that includes provisions for "wasting police time" and making false allegations, the report said.
He had not yet been charged.
McGeever's partner reported him missing in June 2012.
A couple found him wandering on a country road in Ballinamore in Country Lantrim in January, the BBC reported.
He was described as emaciated and barefoot, and to have lost about 70 pounds.
The former tycoon said he had been kidnapped from his home at gunpoint in May 2012. He told the couple he did not know where he was or what the date was.
McGeever told them he had been in a van for a long time before some men dropped him off.