None were ultimately charged when Georgia prosecutors filed a sweeping criminal case against Trump and 18 alleged co-conspirators.
The special grand jury recommended charges against Graham, a longtime senator who represents South Carolina, as well as Georgia's two US senators at the time, Kelly Loeffler and David Perdue, the report said.
Like Trump, all are Republicans.
Graham's office did not immediately respond to a request for comment but said he would speak later on Friday.
The panel also recommended charges against Trump's former national security adviser Michael Flynn, adviser Boris Epshteyn and lawyers Lin Wood and Cleta Mitchell, the report showed.
It was unclear why Fulton County District Attorney Fani Willis opted not to bring charges against the six people, and her office did not immediately respond to a request for comment.
The six were among 39 people the special grand jury recommended charging in its December 15 report, which had been sealed for nine months.
The special grand jury did not have the power to issue charges but Willis used the evidence it gathered to seek an indictment of Trump and his 18 co-defendants from a regular grand jury last month.
Responding to the report's release on Friday, Trump said it showed Willis' case was politically motivated.
"They wanted to indict anybody who happened to be breathing at the time," he wrote on social media.
Trump and the other defendants in the case have pleaded not guilty.
As with his three other criminal prosecutions, Trump has denied any wrongdoing and said he is the victim of political persecution.
Graham, a former Trump rival-turned-golf-buddy, asked Georgia officials to examine absentee ballots after the Republican president's defeat.
Graham has defended his behaviour, saying he was entitled to examine state election activity as chair of the Senate Judiciary Committee.
He fought a subpoena ordering him to testify but was ultimately told to do so by the US Supreme Court.
Loeffler and Perdue, both Trump loyalists, were defeated by Democratic candidates in January 2021 runoff elections.
Perdue ran unsuccessfully for governor in 2022.
Wood, a conservative lawyer who promoted conspiracy efforts about the election, denied wrongdoing and said he was surprised to find out the special grand jury recommended charges against him.
"I'm not quite sure why my name is in it," he told Reuters.
He has since retired in the face of disciplinary bar proceedings.
The special grand jury convened in 2021 at the request of Willis to aid her investigation.
Over several months, the jurors subpoenaed testimony from 75 witnesses, including Trump allies such as his former lawyere Rudy Giuliani, Graham and top Georgia officials such as Governor Brian Kemp.
The special grand jury did not act unanimously.
It voted 13-7, 14-6 and 17-4 in favour of indicting Graham, Loeffler and Perdue respectively.
There was one abstention in each of the votes for Graham and Loeffler.
The grand jury voted 20-1 in favour of indicting Trump with respect to the US effort to overturn the election.
The indictment listed 30 unindicated co-conspirators, who have not been charged but allegedly played a role in the scheme.
Despite his legal troubles, he remains the front-runner for the Republican presidential nomination next year against Joe Biden, the incumbent.
The special grand jury report remained secret at Willis' request while she determined what charges to bring.
With the indictments issued, Fulton County Superior Court Judge Robert McBurney ruled there was no longer any reason to keep it from the public.
