City Press reported on its website that the letter was sent to Zuma on Friday by the miners' lawyers, Maluleke, Msimang and Associates.
Zuma was asked to release the miners by 1pm on Sunday or face an urgent high court application compelling him to release them.
Maluleke, Msimang and Associates reportedly wrote that keeping the miners behind bars was "unlawful".
Justice department spokesperson Mthunzi Mhaga said this would be an "extraordinary" request.
"If they are adopting that stance, it would be an extraordinary route to explore from a legal point of view," he said.
"We would expect them to approach the courts."
Engaging the NPA
He said Justice Minister Jeff Radebe had not seen or received the letter.
"We'll have to wait and see the contents of the letter, because the minister is engaging with the NPA [National Prosecuting Authority] with the view to understand their decisions on the charges."
On August 16, police opened fire on striking workers gathered on a hill near Lonmin's Marikana mine, in North West, killing 34 of them and wounding 78.
Initially, the arrested group was charged with public violence.
On Thursday, the NPA announced they would also face murder and attempted murder charges for the deaths of their colleagues.
The NPA's contentious decision was questioned on Friday.
Radebe said he would seek clarity on the reasons for the move, while legal experts and political parties roundly condemned the decision.
Radebe invoked section 179 (6) of the Constitution, which states that the justice minister "must exercise final responsibility over the prosecuting authority". – Sapa