Mahathir is also racing ahead with an investigation into graft at 1Malaysia Development Berhad (1MDB), a state fund founded by the ousted Najib that is sunk in a multi-billion-dollar graft scandal. Anger over the scandal helped Mahathir's alliance score a stunning election victory last week, ending the 60-year rule of Najib's coalition.
Mahathir, 92 was sworn in as the leader on Thursday, making him the world's oldest democratically elected leader.
On Tuesday, Mahathir said he expected to be prime minister for one or two more years, setting off talk of differences between the two.
"I will play a role in the background even when I step down".
It was reported that the Pardons Board committee will meet at 5pm on Wednesday to discuss the application for a royal pardon for Anwar.
Without the pardon, Anwar would have been banned from politics for five years due to having a criminal record.
Malaysian financier Low Taek Jho has been ordered by a U.S. court to turn over his $250 million yacht "Equanimity" to the U.S. authorities who plan to sail it from Indonesia and sell it in the U.S. The yacht is among more than $1.5 billion in assets that the U.S. claims Low and his accomplices acquired with money they siphoned from 1MDB. He has been in hospital for a few months recovering from a shoulder operation.
Mr Mahathir has promised to step aside for Mr Anwar to become prime minister within two years. He added that he would make the final decision about cabinet posts.
"Mahathir has proven his tenacity, accepted his past limitations, apologised and sacrificed his time and energy to raise the dignity of the people", Anwar wrote in the note on May 8.
Anwar Ibrahim is not rushing back into politics.
Reuters could not verify the report. Anwar's wife, Wan Azizah Wan Ismail, endorsed Mahathir and served as his deputy in the coalition to oust Najib.
"But as a family, we were in concert that we can not expect the people of Malaysia to take a risk for their freedom if we ourselves were not prepared to take those same risks".
In the 1990s, Mahathir was prime minister, Anwar who worked under him was his deputy and clear heir-apparent. Once a high flyer in the ruling party, Anwar was convicted of homosexual sodomy and corruption after a power struggle with Mahathir in 1998.
Mahathir vowed on Monday to investigate any faults that may have been committed by Najib's government and said all ministries had been instructed not to destroy any documents.
Low, a friend of Najib's stepson Riza Aziz, had no official role at 1MDB but USA investigators say he had considerable influence over its dealings and was often in contact with Najib.
"Based on the panel review, we felt the case should not have been closed as there was compelling information to say that the case could be further investigated", Mr Sundramoorthy said.
1MDB is now under worldwide probes in at least six countries, including Switzerland and Singapore, over charges of money laundering and bribery.
Mr Najib and the fund deny any wrongdoing.