"Such a plan is in the works," the source said. Separately, government spokesman Steffen Seibert said that "we are not denying" reports of the planned meeting.
While former US president Barack Obama had labelled Merkel an "outstanding partner", there has been little known contact between the German leader and Trump since he took office.
Following Trump's shock election, Merkel reminded the billionaire of democratic values in their first phone conversation.
Any "close cooperation" must be on the basis of the "values of democracy, freedom, respect for the rule of law and human dignity, regardless of origin, skin colour, religion, gender, sexual orientation or political belief," she said then.
Merkel has also criticised Trump's decision seeking to ban citizens from seven Muslim-majority countries from entering the United States.
In turn, Trump has been a strident critic of Merkel's liberal refugee policy that has led more than a million asylum seekers to come to Germany since 2015.