"We think that within a short while we will have a case against him, we will be able to charge him", he said via video conference to The Wall Street Journal CEO Council Meeting in Tokyo.
Mahathir blocked Najib from leaving the country last weekend.
Mahathir was spurred out of retirement by a corruption scandal at 1MDB, a state fund set up by Najib that is being investigated by the US and several other countries after Najib's associates allegedly stole and laundered $4.5 billion from it.
Ooi Chin Hock, a dealer with SJ Securities, told AFP he believed the "government is supporting the stock market to make sure there is not too much volatility".
Najib has repeatedly denied wrongdoing after 2015 revelations that around $700 million - alleged to be 1MDB funds - appeared in his personal accounts before the prior election in 2013.
"When he is on leave, the solicitor-general will cover his job as the attorney general".
Mahathir has vowed that "heads must fall" in government bodies suspected of colluding in corruption, and on Monday the head of the Malaysian Anti-Corruption Commission - which had targeted critics of Najib - resigned.
1MDB is now under worldwide probes in at least six countries, including Switzerland and Singapore, over charges of money laundering and bribery.
But it has not been all smooth sailing since the historic win, with concerns over the slow formation of the cabinet as different parties in the winning alliance jostle for positions.
On May 10, Mahathir was sworn in as the seventh Prime Minister of Malaysia at the National Palace in Kuala Lumpur.
In remarks on Tuesday, the 92-year-old said that Anwar - a former enemy turned ally - may just join the cabinet for a while after his expected release from prison on Wednesday. He has agreed to hand over power to jailed reformist leader Anwar Ibrahim but has not previously given any timing. Questions over how long he plans to stay on as prime minister risk undermining an agenda that included scrapping a goods-and-services tax, reviewing large infrastructure projects and cutting spending.
The law, which was rushed through parliament last month ahead of last week's general election, carries a stiff penalty of up to six years in jail and a fine of 500,000 ringgit ($128,000).
He said that it would be given a clear definition but that there was a "limit" to press freedom, despite having pledged during the election campaign to abolish it.