Dr Mahathir's accusations of ruling party leaders accepting bribes "warrant police action", a spokesperson said.
Dr Mahathir and the Bersih pro-democracy movement have called for current PM Najib Razak to resign over corruption allegations.
Tens of thousands attended Bersih's weekend rallies across the country.
A spokesman for Dr Mahathir, Sufi Yusoff, told Reuters: "As far as I am aware he has not been approached by the police yet. We will comply with the police on whatever is needed."
It was unclear whether Dr Mahathir could face charges.
Dr Mahathir delivered a speech on Saturday at the rally in the capital, Kuala Lumpur, where he called for a "people's power" movement to topple Mr Najib, a former ally.
Mr Najib has denied all allegations of corruption and has accused Dr Mahathir of mounting a political smear campaign against him.
Read more: 1MDB, the case that's riveting Malaysia.
Dr Mahathir was Malaysia's longest serving prime minister, in office from 1981 to 2003, and remains highly influential. The 90-year-old used to lead Mr Najib's party, Umno.
Police Inspector-General Khalid Abu Bakar told reporters that, during his speech at the Bersih rally, Dr Mahathir had made "all sorts of accusations", including one that alleged Umno division chiefs had received bribes.
"We want to know further and where he had obtained the information... I hope he will give his co-operation," said Mr Khalid.
He added that other prominent figures who attended the officially illegal rally, as well as the organisers, would also be called up for questioning.
Mr Najib has repeatedly denied taking money from Malaysia's state investment fund, 1MDB.
The anti-corruption agency has effectively cleared him, saying the $700m (Â£455m) found in his personal accounts came from foreign donations.
Malaysian police have said they will ask former PM Mohamad Mahathir to give a statement on allegations he made at a recent anti-government protest.