Muhyiddin Yassin was offered the prime minister's post after the last general election, according to his special functions officer Marzuki Mohamad.
However, the Bersatu president rejected the offer out of respect for Dr Mahathir Mohamad and due to the promise that the latter would be the prime minister if Pakatan Harapan won the polls.
In a Facebook posting, Marzuki said the offer was made by an "influential individual" whom he did not name.
He was responding to Tamrin Abdul Ghafar, who had penned an article on the formation of Bersatu, which Marzuki claimed portrayed Muhyiddin as a power-crazed politician who wanted to prevent Mahathir from becoming prime minister.
Tamrin is the son of the late Ghafar Baba, who served as Mahathir's deputy from 1986 to 1993 during his first tenure as prime minister.
"I do not know when Tamrin was in Bersatu.
"Perhaps because he was not in Bersatu, he is not aware of the real history (of the party)," added Muhyiddin's aide.
Marzuki said during the time when Bersatu had not named Mahathir as the candidate for prime minister, several supreme council members sought Muhyiddin's stand as they felt he was also qualified for the post.
"But Muhyiddin was firm in stating that there is nobody more qualified than Mahathir to be the prime minister candidate.
"In fact, Muhyiddin was the first person to state during the supreme council meeting that Barsatu officially names Mahathir as the candidate. The rest is history," he added.
Earlier today, Muhyiddin stressed there was no rift between Mahathir and him.
Speculation of strained ties between the two surfaced following the reshuffle of the Johor executive council.