"The announcement is expected to be made on Monday," McClatchy news reported on Friday. "Mulvaney would need to be confirmed by the Senate."
Mulvaney was elected in November to a fourth term in Congress from the US state of South Carolina, overwhelmingly defeating Fran Person, who was backed by his former boss, US Vice President Joe Biden.
The Charleston Post & Courier, which confirmed the report, noted that Mulvaney was the second official from the state named to a senior post in the Trump administration.
Trump previously tapped Governor Nikki Haley to be US Ambassador to the United Nations.