A warrant was issued for his arrest last Friday, after he failed to appear in court on two charges of bigamy.
Then, yesterday, Mandela again failed to report to the Bityi police station.
Station commander Lieutenant-Colonel N Ngame has now written to police in Goodwood, Cape Town, asking them to serve the warrant at his address in the Acacia Park parliamentary village or to arrest him on sight.
". it has become crystal clear that this person is evading justice," Ngame said.
It is understood that Mandela, an ANC MP, is in Cape Town, where parliament resumes work today.
Both police and the National Prosecuting Authority have denied the warrant, but the Daily Dispatch is in possession of a copy.
Speaking on behalf of the Mandela family, attorney Gary Jansen said: "These are legal matters, not media matters, and they are taking their legal course."
Mandela was unavailable for comment.
Mandela's estranged first wife, Tando Mabunu-Mandela, laid charges of bigamy after he defied the court to marry a second and third woman. Both marriages have since been annulled.
Mabunu-Mandela's attorney Wesley Hayes said it has been a constant battle to get Mandela to cooperate.
"Mr Mandela seems to think he is above the law," Hayes said yesterday.