Reports of Acosta's nomination came a day after Trump's first choice for labor secretary, Andy Puzder, withdrew himself from consideration amid concerns he would not gather enough votes in the Senate to be confirmed.
In a statement, Puzder said he made the decision to withdraw after careful consideration and discussions with his family. Harward would replace Flynn, who resigned after revelations that he had discussed USA sanctions on Russia with the Russian ambassador to the United States before President Donald Trump took office.
Puzder's nomination was subject to fierce opposition by Democrats and progressive groups.
If confirmed, Acosta will be the only Hispanic person in Trump's cabinet.
But Republicans, too, had grown tired of the range of liabilities facing Puzder, and senior GOP officials informed the White House Tuesday night and Wednesday that Puzder lacked a viable path for confirmation. Their inability to support him would have placed the nomination in jeopardy since Republicans have only a 52-48 majority in the Senate.
After five separate delays, his confirmation hearing before the Senate Health, Education, Labor and Pensions Committee was scheduled for Thursday. While Puzder is a public figure who is seeking a high government office, Fierstein says she is not, and shouldn't have to go through this.
Acosta is an attorney who has worked in government in the past. The double Harvard Acosta also served as a clerk to Justice Alito when Alito sat on the Third Circuit, where Acosta let down the judge by failing to understand sports. But despite all that, Republicans were still on board with Puzder until a videotape surfaced of his ex-wife, Lisa Fierstein, alleging spousal abuse while in disguise on a 1990 talk show.