In a tweet posted Friday, Lingling Wei, a China economics correspondent at the Wall Street Journal, said the U.S asked China to reduce its trade surplus by at least $200 billion by year-end 2020, citing a document issued to the Chinese before the talks.
President Donald Trump has often called on China to reduce its bilateral trade deficit by $100 billion a year.
The U.S. trade envoy also wanted China not to target U.S. farmers and agricultural products and sought assurances from the Asian giant that it would not retaliate over restrictions on investments from Beijing, Wei said.
The U.S. Commerce Department was not immediately available for comment when contacted by CNBC on Friday.
In response to the U.S. demands, China offered to lower duties on goods such as cars in an effort to resolve an escalating trade dispute with Washington, Reuters reported citing two sources with knowledge of the matter.
China also reportedly asked the U.S. to treat investments from Beijing equally in its national security reviews and stop issuing new restrictions on investments.
Ahead of Friday's talks, Mnuchin said U.S. trade officials were having "very good conversations" with their Chinese counterparts.
Shortly before Mnuchin's arrived in China on Thursday, Trump tweeted: "Our great financial team is in China trying to negotiate a level playing field on trade! I look forward to being with President Xi in the not too distant future. We will always have a good (great) relationship!"
It was not immediately clear when Trump and Chinese President Xi Jinping will next meet, although both global players are set to attend some of the same multilateral events later this year — including the G-20 Summit and APEC.