On trade they will commit to fighting protectionism but will also allow "legitimate" measures to protect their markets, the source said on the final day of the talks in Germany.
The outcome represents a compromise with Trump who wants to do more to protect domestic companies from foreign competition through his "America First" policy.
However on climate change negotiators remain at loggerheads following Trump's decision to withdraw the US from the 2015 Paris climate accord, the source said.
The sticking point in the communique is about fossil fuels -- blamed for global warming -- with the US side wanting to be able to continue to export and promote their use.
"The idea now is to find a good balance of language -- it will be discussed this morning," the source said on condition of anonymity.
G20 leaders had a tough time reaching consensus on climate and trade policy despite a plea from Merkel to other leaders to compromise in talks that have pitted Trump against virtually every other country in the club of leading economies.
As well as resolving the differences over trade and climate change, Merkel must lead discussions on migration on Saturday - issues that have become more contentious since Trump entered the White House half a year ago promising an "America First" approach.
Last month, he pulled the United States out of a landmark international agreement aimed at combating climate change. And he is threatening to take punitive trade measures in the steel sector which would hit China, Germany, Canada and a host of other countries.
Climate conundrum
Envoys have been working for weeks to bridge differences, and European sources said they came up with new language on the climate issue on Thursday which would be put to the leaders for approval.
The latest draft communique sticks with language about the Paris climate accord being "irreversible" but removes a reference from an earlier version to a "global approach" that some countries felt could suggest there was a parallel track to Paris.
It also includes a new paragraph which says the United States will "work closely with other partners to help their access to and use of fossil fuels more cleanly and efficiently". Some experts were skeptical whether leaders would approve the reference to fossil fuels, which would be a clear nod to Washington.
Police send reinforcements
As the leaders met on Friday, police said they were sending reinforcements from other parts of Germany to cope with thousands of anti-capitalist protesters who set fire to cars, rubbish bins and wooden pallets in violence that Hamburg's interior minister called "frightening".
Merkel chose Hamburg, the port city where she was born, to send a signal about Germany's openness to the world, including its tolerance of peaceful protests.
The summit is being held only a few hundred meters from one of Germany's most potent symbols of left-wing resistance, a former theater called the "Rote Flora" which was taken over by anti-capitalist squatters nearly three decades ago.
Police said 196 officers had been injured, 83 protestors temporarily detained and another 19 taken into custody.
