The U.S. and China will hold a new round of principal-level talks next week in a bid to finalize "phase one" of their trade deal in November, Treasury Secretary Steven Mnuchin told CNBC in an Oct. 14 interview.

Deputy-level calls are expected to be held this week before Mnuchin and U.S. Trade Representative Robert Lighthizer hold a phone call with Chinese Vice Premier Liu He next week.

"My expectation is we'll have the deputies meet between now and Chile, and my expectations are that we will be meeting with the vice premier in Chile before the presidents meet to finish the deal," Mnuchin added. He stressed that the U.S. and China had reached a "fundamental agreement" on trade that remained "subject to documentation" following last week's high-level negotiations.

Mnuchin's latest remarks come after Beijing was reportedly eyeing further discussions as soon as the end of the month ahead of the Asia-Pacific Economic Cooperation summit in November in Chile.