The gesture was "outrageous," the publication quoted an unnamed German minister as saying.
"The concept behind putting out such demands is to intimidate the other side, but the chancellor took it calmly and will not respond to such provocations," the minister is further cited as saying.
Read alsoMcCain "optimistic" over prospects of U.S. lethal aid to UkraineAccording to the Times, the bill handed to Merkel was thought to be for more than $300 billion. It was reportedly calculated by adding the amounts by which Germany have fallen short on annual payments to NATO since 2002 — and adding interest.
Each NATO member is meant to spend 2% of their gross domestic product annually on defense. Germany is increasing military spending, but its contribution is still seen falling well short of the 2% goal this year.
Last week, Berlin struck back at Trump’s claim that Germany owes "vast sums" to NATO.
"There is no account where debts are registered with NATO," German Defense Minister Ursula von der Leyen said in a statement, questioning how military spending was calculated and arguing that a country's financial commitment to the military alliance is not the only measure.
"Defense spending also goes into U.N. peacekeeping missions, into our European missions and into our contribution to the fight against ISIS terrorism," von der Leyen said.