Trump has said that the US and China have made progress on a deal requiring TikTok's US assets to be transferred to local owners from China's ByteDance.
TikTok counts 170 million users in the United States and helps shape public discourse on politics and culture.
Trump praised the group in an interview with Fox News, calling them prominent people and "American patriots".
"I think they're going to do a really good job," Trump said, crediting TikTok with helping build his support among young voters in the 2024 presidential election.
Murdoch, the CEO of Fox Corp, recently cemented long-term control of his family's media empire that includes Fox News and the Wall Street Journal after settling a years-long legal battle with his siblings.
The family patriarch, 94-year-old Rupert Murdoch, may also be involved in the deal, Trump said.
Rupert and Lachlan Murdoch's news outlets attract conservative-leaning audiences but they have occasionally drawn Trump's ire.
Trump sued the Wall Street Journal and Rupert Murdoch for defamation over a July report that said Trump signed a 2003 birthday greeting for late financier and convicted sex offender Jeffrey Epstein that included a sexually suggestive drawing and a reference to shared secrets.
The newspaper has defended its reporting and vowed to fight the lawsuit.
Ellison, the co-founder of Oracle and a major Republican donor, has long been linked to a potential TikTok deal.
Dell is the CEO of Dell Technologies.
On Saturday, White House press secretary Karoline Leavitt said Oracle would be responsible for TikTok's data and security and that US citizens will control six of the seven seats for a planned board.
Trump's administration has declined to enforce a US law enacted during his predecessor's administration requiring TikTok's divestiture over fears its US user data could be accessed by the Chinese government.
Trump has included negotiations over the app as part of wide-ranging economic talks with China.
Trump's administration has made a series of unusual interventions in US business, including taking a 10 per cent stake in Intel Corp and allowing AI chip giant Nvidia to sell its H20 chips to China in exchange for receiving 15 per cent of those sales.
Trump has defended those moves as benefiting US interests.
Critics, including some business leaders and Republican lawmakers, have called the interventions a stark departure from the norms of capitalism and said they risk hurting the competitiveness of the US economy.
with AP
