Kerry is the first senior official from Biden administration to visit China, Global Times said.
Kerry's trip is seen as a chance for Beijing and Washington to put aside high political tensions - following a heated initial meeting last month between diplomats in the United States - and focus on areas of potential climate collaboration.
President Joe Biden has made scuttling the climate-sceptic policy of his predecessor Donald Trump a priority.
In Shanghai, officials are expected to discuss environmental challenges, areas which both China and the USA say are top priorities, as well as the upcoming UN-led climate talks to be held in Glasgow at the end of the year.
The summit comes as it seeks to shore up its leadership on global issues, such as climate change - an area where Washington's commitment had receded due to former President Donald Trump's formal withdrawal from the Paris Agreement late previous year.
The United States is renewing a call that all nations including the USA and China "must raise their ambitions" on carbon neutrality, as officials from the world's two largest emitters held talks in Shanghai on Thursday.
He will be meeting his Chinese counterpart Xie Zhenhua, Reuters reported. Weeks after Biden took office, the U.S. rejoined the accord.
The spokesperson added China "is not yet on a path that will allow the world to meet the Paris Agreement's goal of holding the increase in the global average temperature to well below 2 degrees Celsius and pursue efforts to limit the temperature increase to 1.5 degrees Celsius".
"Both countries have a long way to go to firm up their targets and commitments for this decade", said Myllyvirta.
"Tackling climate change is a shared responsibility. and should not become a geopolitical bargaining chip or used to attack other countries (or impose) trade barriers", Xi told France's Emmanuel Macron and Germany's Angela Merkel on the sidelines of a virtual climate summit Friday, according to state broadcaster CCTV.
"There needs to be a reverse on that", he said.