Musk had indicated that he planned to start his donations in July to the America PAC, backing former President Donald Trump's presidential run, the newspaper said. However, the South Africa-born businessman was not listed on a Monday filing by the group, which shows that it has raised more than $8 million.
Lonsdale Enterprises and the Winklevoss Twins were among the donors to America PAC. Lonsdale donated $1 million and Cameron and Tyler Winklevoss each contributed $250,000.
Musk and Lonsdale did not respond to Reuters' request for comments.
On Saturday, Musk publicly endorsed Trump for the first time in the U.S. presidential race, hours after Trump was shot in the ear during a campaign rally.
This move cements Musk's shift towards right-wing politics and gives Trump a high-profile backer in his bid to return to the White House in the Nov. 5 election.
Trump on Monday chose Ohio U.S. Senator J.D. Vance to be his vice presidential running mate, as the Republican Party officially nominated the former president to run again for the White House.