Asked to confirm rumors that Wolf, a department undersecretary, would assume the role, Trump told reporters: "Well he's right now acting and we'll see what happens. We have great people in there."
Trump announced the resignation of his current acting secretary, Kevin McAleenan, three weeks ago, marking the latest departure in a long list of top officials to leave his administration.
"As the president has said, Kevin McAleenan has done a tremendous job. He'll be leaving after Veterans Day and after he departs, Chad Wolf will serve as acting secretary in the interim," White House spokesperson Hogan Gidley said.
McAleenan served in the role for six months, replacing Kirstjen Nielsen, who sat at the helm of the powerful agency for 18 months.
Green card holders included in Trump ban: Homeland Security
Homeland Security is the third-largest department in the US government, overseeing a number of agencies including the Coast Guard, Secret Service and FEMA, which handles disaster preparedness, coordination and support.
In addition, it is in charge of immigration-related agencies such as Customs and Border Protection, Immigration and Customs Enforcement (ICE) and Citizenship and Immigration Services.
Wolf, who is the undersecretary for the department's Office of Strategy, Policy and Plans, has "made significant progress to strengthen US border security, address the humanitarian crisis on the US Southwest Border, and improve the integrity of the US immigration system" a biography on the DHS website says.
He will be the fifth official under Trump to lead the department, which was created in 2002.
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