Trump made the announcement on his social media platform Truth Social.
Lutnick is a co-chair of Trump's transition team, along with Linda McMahon, the former wrestling executive who previously led Trump's Small Business Administration.
Both are tasked with putting forward candidates for key roles in the next administration.
The nomination would put Lutnick in charge of a sprawling cabinet agency that is involved in funding new computer chip factories, imposing trade restrictions, releasing economic data and monitoring the weather.
It is also a position in which connections to CEOs and the wider business community are crucial.
An advocate for imposing wide-ranging tariffs, Lutnick told CNBC in September that "tariffs are an amazing tool for the president to use - we need to protect the American worker".
Trump on the campaign trail proposed a 60 per cent tariff on goods from China - and a tariff of up to 20 per cent on everything else the United States imports.
Mainstream economists are generally sceptical of tariffs, considering them a mostly inefficient way for governments to raise money and promote prosperity.
Lutnick had been considered for treasury secretary, a role that has been at the centre of high-profile jockeying within the Trump world.
At the same time, the treasury position is closely watched in financial circles where a disruptive nominee could have immediate negative consequences on the stock market.
The news comes after Elon Musk and others in Trump's orbit called on Trump to dump previous front-runner for treasury secretary, Scott Bessent, in favour of Lutnick.
Musk said in his post that "Bessent is a business-as-usual choice, whereas @howardlutnick will actually enact change".
with AP
