Trump has not announced his nominee for the role but Lutnick and investor Scott Bessent are serious contenders for the job and sources familiar with his thinking say Trump has been wrestling with picking one of the two or considering another option.
Musk said Bessent is "a business-as-usual choice".
"Business-as-usual is driving America bankrupt, so we need change one way or another," Musk said on X.
"Would be interesting to hear more people weigh in on this for Trump to consider feedback."
Would be interesting to hear more people weigh in on this for — Elon Musk (@elonmusk) @realDonaldTrump to consider feedback.My view fwiw is that Bessent is a business-as-usual choice, whereas @howardlutnick will actually enact change. Business-as-usual is driving America bankrupt, so we need change… https://t.co/igGLZOJ8wzNovember 16, 2024
Both Lutnick and Bessent have been mentioned as possible picks to lead the Treasury department.
Bessent is considered the more conventional business-friendly choice.
He is sceptical about cryptocurrency while Lutnick has suggested it could be used for people to pay their taxes.
A short time later, Trump's pick to lead his Health and Human Services Department, Robert F Kennedy Jr, also appeared to endorse Lutnick, posting on his own X account, "Bitcoin is the currency of freedom, a hedge against inflation for middle class Americans."
"Bitcoin will have no stronger advocate than Howard Lutnick," he wrote.
Bitcoin is the currency of freedom , a hedge against inflation for middle class Americans,a remedy against the dollar's downgrade from the world's reserve currency, and the offramp from a ruinous national debt. Bitcoin will have no stronger advocate than Howard Lutnik.— Robert F. Kennedy Jr (@RobertKennedyJr) November 16, 2024
Treasury is arguably the most important slot Trump has left to fill but he is also yet to announce choices for others, including the heads of the Education and Labor Departments.
Musk has been increasingly influential in Trump's inner circle and has been staying at the president-elect's Mar-a-Lago club in Palm Beach, Florida, as Trump forms his incoming government.
At a gala event on Thursday night, Trump teased Musk about his ongoing post-election stay at Mar-a-Lago.
"I can't get him out of here. He just loves this place. And I like having him here," Trump said.
At the end of the event, Musk mounted the stage.
"The public has given us a mandate that could not be more clear. The people have spoken, the people want change," he said.
Lutnick has been helping Trump with his transition efforts.
He has praised the president-elect's economic policies, including his use of tariffs.
with AP