President Trump announced Thursday morning that he will hold a press conference at the White House at noon.
After more than a decade in public service, Acosta has beens serving as the dean of the Florida International University Law School.
Acosta is Trump's first Hispanic nominee to his Cabinet.
Perhaps especially important for Trump, who has had trouble getting his cabinet nominees through confirmation, Acosta's already been to the Senate committee rodeo - he has served in three providentially-appointed, senate-confirmed positions in the past.
Joseph Guzman, an assistant professor at Michigan State University, and Catherine Templeton, former head of the SC labor department, were also potential candidates, Bloomberg reported, citing a White House official.
Puzder, the CEO of CKE Restaurants, which owns the Hardee's and Carl's Jr. brands, is a vocal critic of President Barack Obama's labor policies and the Fight for $15.
Puzder's confirmation hearing was scheduled for Thursday.
A number of issues concerning Puzder turned off the majority-Republican congress, including details that he hired an illegal immigrant as a housekeeper and failed to pay taxes on her until he was nominated. Acosta was the subject of some controversy after it was revealed his office illegally recorded conversations carried out between a defense attorney and a defendant, who was later acquitted. In the 1990 episode, wearing an elaborate disguise, Fierstein detailed physical abuse she said Puzder inflicted on her during their marriage.
The main sources of criticism were believed to be allegations from Puzder's messy divorce, his hiring of an undocumented worker in his home, his support for increased automation and his company's racy advertisements.