The winning proposal will be "connected to" the University of Chicago, although the site has not been decided on yet, NBC in Chicago reports.
The president was a law professor at the university and still has a home on the city's South Side.
The library will store his papers and help frame his legacy as president.
A formal announcement will be made the week after next, reports CBS.
It says the president indicated he was leaning towards choosing his hometown in a recent phone call with Chicago Mayor Rahm Emanuel, once his closest adviser at the White House.
Mr Obama met his wife, First Lady Michelle, when working at a law firm in the city in 1989.
The losing cities also have strong connections to the Obama story - he grew up in Hawaii and attended Columbia University in New York.
The other Chicago bid that completed the shortlist of four was from the University of Illinois.
The 13 presidential libraries - spanning from Herbert Hoover to George W Bush - are administered by the US National Archives.
Former President Bill Clinton's presidential library is in Little Rock and George W Bush has one at the Southern Methodist University in Dallas.
All five living presidents gathered for the dedication of the Bush library in 2013, a ceremony that moved Mr Bush to tears.
Chicago has beaten New York City and Hawaii as the chosen location for President Barack Obama's library, according to US media.