Greg Craig, a former special counsel to Bill Clinton, the former president, will become White House counsel when Obama takes office in January.
Daschle served as a co-chair and adviser on Obama's presidential campaign, recently wrote a book on healthcare and is currently working with former senate majority leaders on recommendations to improve the healthcare system.
He served as the top Democrat in the senate between 1994 and 2004, and was majority leader when Democrats controlled the senate between 2001 and 2003.
After losing a bid to keep his senate seat in 2004, he has worked as a public policy adviser for the US law firm Alston and Bird.
Daschle was an early supporter of Obama, encouraging the senator from
Illinois to make his presidential bid.
If confirmed in the role, Daschle would play a central part in Obama's plans to extend healthcare coverage to the 47 million Americans who lack medical insurance.
He is currently being vetted by Obama's team to ensure there are no possible conflicts of interest ahead of the president-elect's inauguration on January 20, officials told AP.
The report follows widespread rumours over several key cabinet posts in Obama's administration, including reports on Tuesday that Eric Holder, former deputy attorney general under Bill Clinton, the former US president, could become the first African-American to head the US justice department.
Holder has reportedly accepted a conditional offer from Obama, a senior Democrat told news agencies on Tuesday.
And there have been several claims that Hillary Clinton, the New York senator and former Democratic rival of Obama's for the presidential nomination, has been offered a role as secretary of state, but none of the reports have been confirmed.