"The president wants to put America's needs first, both from a national security and economic perspective," White House press secretary Karoline Leavitt told reporters.
The potential deal could involve swapping government grants for Intel shares, according to US Commerce Secretary Howard Lutnick.
The highly unusual move could help Intel as it struggles to compete with rivals like Nvidia, Samsung and TSMC, particularly in the booming artificial intelligence (AI) chip market.
The US wants a stake Intel in exchange for grants approved during the Biden administration, Lutnick said on CNBC on Tuesday.
"We should get an equity stake for our money," he added. "We'll get equity in return for that... instead of just giving grants away."
The potential deal, which was first reported last week, aims to help Intel build a flagship manufacturing hub in the US state of Ohio. At the time, a White House spokesman told the BBC that the reports "should be regarded as speculation" unless officially announced.
Last week, Intel did not comment directly about reports but said it was "deeply committed to supporting President Trump's efforts" to strengthen manufacturing and technology in the US.
On Monday, Japanese investment giant Softbank said it would buy a $2bn (£1.5bn) stake in Intel, in a move that some analysts said is a sign of confidence in the firm's turnaround.
After that announcement, the firm's shares rose by almost 7% in New York on Tuesday.
Intel is one of the few American companies capable of producing high-end semiconductors at scale but the company has fallen behind global rivals.
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