"A delegation will travel to the United States this week or next week to discuss removing Sudan from its state sponsors of terrorism list," Burhan said in his first interview on state television since taking power.
Burhan took the helm after predecessor General Awad Ibn Ouf stood down less than 24 hours after becoming military council chief, following the ouster of long-time president Omar al-Bashir.
The United States lifted its 20-year-old trade embargo imposed on Sudan in October 2017.
But Washington kept Sudan in it state sponsors of terrorism list along with Iran, Syria and North Korea.
It had included Sudan in the blacklist in 1993 for Khartoum's alleged links with Islamist militants.
Al-Qaeda founder Osama bin Laden lived in Sudan between 1992 and 1996.
Washington, however, has praised the country's new military leader for freeing political prisoners, and on Thursday announced plans to dispatch an envoy to Khartoum to encourage a transition to democracy.
On Thursday State Department spokeswoman Morgan Ortagus said that the United States will "calibrate our policies based on our assessment of events" but added that talks on delisting Sudan as a state sponsor of terrorism remained suspended.
"The will of the Sudanese people is clear: it is time to move toward a transitional government that is inclusive and respectful of human rights and the rule of law," she said.
A senior US official, speaking on condition of anonymity, said at the time that the short-term US goal was to "get the military folks out of center-stage" and "back to being responsible for security, nothing else."
"Longer term is to make absolutely sure that whichever group is going to be responsible for the transition prepares a transition implementation that will lead to a truly democratic government that will reflect the will of the Sudanese people," he said.
The United States had included Sudan in the blacklist in 1993 for Khartoum's alleged links with Islamist militants.