NBC cited sources as saying that under an agreement US officials reached recently with Turkey, Brunson would be released after certain charges against him were dropped at his next court hearing.
While Brunson's October 12 hearing was already scheduled weeks in advance, analysts say his possible release comes at an opportune time for Turkey, which is looking to win support from the U.S.as it faces a political crisis with the Saudis.
The pastor was imprisoned for almost two years before being placed under house arrest on July 25 for health reasons.
According to the NBC report, Trump administration officials aren't "fully confident" that Turkey will actually go through with the agreement.
Ismail Cem Halavurt, lawyer of the jailed pastor Andrew Brunson, talks to media outside the Aliaga Prison and Courthouse complex in Izmir, Turkey May 7, 2018.
The US has been adamant that Brunson is innocent and has repeatedly asked Turkey to free him.
The deal is said to include a commitment by the U.S.to ease economic pressure on Turkey.
The Thursday comments come a day after US Secretary of State Mike Pompeo said he was hopeful that Turkey would release the pastor soon, ending a two-year detention that has shaken relations between the one-time allies.
In a Middle East Eye report in late September, Turkish and USA officials said they were working to free Brunson.
Brunson has been held for nearly two years trumped-up on wide-ranging charges of conspiring to overthrow the Turkish government.
"I am very hopeful that before too long Pastor Brunson will, he and his wife will be able to return to the United States", Pompeo said at an event Wednesday.
Brunson, of Montreat, N.C., faces up to 35 years in jail if convicted.
Officials remained cautious, however, in light of a deal that fell apart last summer, with both sides blaming each other for acting in bad faith. "We hope to solve the matters between us as soon as possible and develop ties with the U.S.in politics and the economy once again, in line with the spirit of being strategic partners".
"We remain hopeful that with the court proceeding tomorrow that Turkey will see its way clear and free this good man who is guilty of nothing and who has been incarcerated for several years in Turkey unjustly", Pence said.
The U.S. and Mr. Brunson deny he had anything to do with it.
"Our strategic partnership, which has gone through difficulties so many times, will overcome this turbulent period", Erdogan said during an address at an investment conference held by the Turkey-US Business Council, according to Turkey's state-run Anadolu news agency.
"The Khashoggi affair adds a new variable to a complex question the US and Turkey had already found quite hard to solve".
The U.S. continues to refuse Ankara's demands that the cleric Gulen be extradited.