The US treasury post - that Geithner is tipped to occupy - is considered one of the most powerful in government, and is now tasked with managing a massive $750bn financial rescue package for faltering US financial institutions.
US stock markets rose sharply when Geithner's name was linked to the post on Friday, a sign that the move would be popular on Wall Sreet.
Obama is also set to announce details of a new stimulus plan to help boost the struggling US economy, which many analysts have said is already likely to be in recession.
US economic woes have worsened since Obama won the presidential election on November 4, with unemployment rising sharply, the government taking part-ownership of banking giant Citigroup, and struggling car makers asking for a $25bn bailout to keep them afloat.
Austan Goolsbee, a senior adviser to the president-elect, said Obama was putting together "the most experienced, expert team on crisis management that probably has ever existed in an economic field in the White House".
"But there's one president at a time. I mean, the president-elect is not introducing legislation. He's not able to do anything. We've got to be mindful of that," he told MSNBC.
On Saturday, Obama announced plans to create 2.5 million new jobs as "an early downpayment" on promised reforms.
He said he intended to put people back to work rebuilding roads and bridges, modernising schools, building wind farms, solar panels and fuel-efficient cars - part of a plan to break the US addiction on foreign oil.