Inspector-General of Police Khalid Abu Bakar said police had received several reports regarding the blog post.
"We have begun investigation a few days ago. If there is a case we will refer it to the Attorney-General," the police chief said without elaborating further.
In his post on February 5, Mahathir alleged that Attorney-General Mohamed Apandi Ali had been appointed improperly.
He said Apandi has no credibility after he cleared Najib of any criminal offences or corruption arising from a graft probe into a USD 681 million deposit in his personal bank account.
Mahathir, who was premier for 22 years before he stepped down in 2003, is a severe critic of Najib.
He hastaken his campaign against Najib a step further by becoming the patron of the Coalition of Umno Branch Chiefs Malaysia (GKCM) that is working to oust the prime minister and Umno president.
The group, which claimed to be represented by Umno branch leaders from all over the country, was formed last November to press Najib to step down.
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