Donald Trump and Elon Musk Photographers: Al Drago; Andrew Harrer/Bloomberg Photographer: Al Drago; Andrew Harrer/Bloomberg 
The two have discussed ways for Musk, who runs the social media platform X as well as SpaceX and Tesla TSLA.O, to have "formal input and influence" over economic and border security policies, according to the Journal.
The WSJ also said Musk informed Trump about his ongoing influence campaign aimed at convincing powerful U.S. business leaders not to support Democratic President Joe Biden, who beat Trump in the 2020 election and is seeking a second term.
Those talks, which included billionaire investor Nelson Peltz, also included discussions about funding a "data-driven project to prevent voter fraud," the outlet said, adding no further details were known.
Representatives for Trump and Musk did not immediately respond to requests for comment. Representatives for the Biden campaign also did not immediately respond.
Trump campaign spokesperson Brian Hughes told the Journal that only Trump will decide "what role an individual plays in his presidency." The WSJ said Musk did not respond to its requests for comment.
In March, following a meeting with Trump in Florida, Musk — one of world's wealthiest individuals — said he would not donate money to Trump or Biden. Instead, he aims "to use his clout ... to help defeat Biden by galvanizing the support of influential allies", said the WSJ, citing a person familiar with his thinking.
Musk in recent years has more fully embraced the Republican Party.
Musk has said, without evidence, that Biden is intentionally allowing migrants to cross the U.S.-Mexico border. He has also endorsed antisemitic comments on X, though Musk has denied being antisemitic.
While he has publicly criticized Biden policies on immigration, electric vehicles and tariffs, Musk has not made any formal endorsement in November's contest and Trump has said he did not know if he has the billionaire's support.
Musk's views have hurt his standing among some consumers, according to a CivicScience survey shown exclusively to Reuters.
Trump, a prolific user of Twitter, now X, before he was banned from the social media site following the Jan. 6, 2021, attack on the U.S. Capitol, launched his rival Truth Social platform, owned by Trump Media and Technology Group Corp DJT.O.
(Reporting by Tim Reid, Manas Mishra and Stephanie Kelly; Writing by Susan Heavey; Editing by Lisa Shumaker)