They are being held over a corruption investigation, it adds.
One of those named, industrial tycoon Issad Rebrab, denied the arrest on Twitter, saying he went to the police to sort out a business matter.
Mr Bouteflika, who had been in power for 20 years, resigned three weeks ago following anti-government protests.
The four others who have been detained are brothers from the Kouinef family, named as Reda, Tarek, Abdel Kader and Karim. They are thought to have close links with the former president.
Fresh elections are expected in July.
Their detention comes after the head of the army, Lt Gen Gaïd Salah said last week that some among the ruling elite could be questioned over alleged corruption, Reuters news agency reports.
Protesters who had been demanding the resignation of Mr Bouteflika, had also been calling for the downfall of "Le Pouvoir", or the establishment, meaning that all those around the former president should also go.
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