The EU source said leaders from both sides had no problem with on the climate issue as both sides want to boost efforts to implement the 2015 Paris agreement following President Donald Trump's decision to pull Washington out of the deal.
But "they did not sign (the climate statement) due to the fact they did not agree on market economy status," the source told AFP on condition of anonymity.
When China joined the World Trade Organization in 2001, it was written into the terms of the deal that member states could treat it as a non-market economy for 15 years.
Beijing has said previously that the refusal to grant China market economy status is an example of "covert protectionism" and "double standards" by the West.
In a joint draft summit statement AFP saw earlier this week, China and the US said they would "significantly intensify" their political, technical, economic and scientific cooperation on climate change and clean energy.
The goal is to help the world shift to an economy based on low greenhouse gas emissions, according to the draft.
Disclaimer: No Business Standard Journalist was involved in creation of this content