News weekly Der Spiegel reported that Merkel told a parliamentary committee that she doubted the Afghan army and police would be ready to take over by the time the final German troops are slated to withdraw.
She said the complete withdrawal in 2011 of US troops from Iraq, which is now engulfed in Islamist violence, served as a cautionary tale and wanted to talk to Washington about an extension of the mission beyond 2016, according to a Spiegel source.
Germany's military, the Bundeswehr, is scheduled to leave its biggest camp in Mazar-i-Sharif in northern Afghanistan
, by the end of 2015.
Meanwhile, Germany's foreign minister said on Sunday that Berlin had made serious mistakes in its military engagement in Afghanistan since 2001 and warned against a hasty withdrawal.
Ahead of the end of US-led NATO combat operations in the war-ravaged country this year, Frank-Walter Steinmeier offered a sobering assessment of the 13-year mission.
"There is a lot to indicate that our biggest mistake was to create expectations that were too high," he wrote in a column for the weekly Frankfurter Allgemeine Sonntagszeitung.
"We not only wanted to snuff out the security threat that Afghanistan represented but also lead the country at high speed into a future according to our own vision."
He said that despite progress in Afghanistan, the country was still plagued by a thriving drug trade and rampant corruption.
Warlords hold power in several provinces and violence abounds, Steinmeier added, lamenting that the extremist Taliban had been "long been underestimated as a political player".
But he said the deployment should not be seen as a failure, noting that compared to the situation in Syria or Iraq "the results in Afghanistan are fairly respectable".
And he cautioned against "hastily leaving the country, like the Americans did in Vietnam in 1975".
Amid calls for Germany to match its economic might with more military muscle in the world's trouble spots, Steinmeier said there were clear conclusions to be drawn from Afghanistan.
"We must engage more decisively, not only look at military aspects," he said.
"But we also need humility. We must accept sometimes how little can be changed from the outside."
Steinmeier served as chief of staff to then chancellor Gerhard Schröder when Germany offered the United States "unlimited solidarity" in the wake of the September 11th, 2001 attacks.
Germany has been the third-largest contributor of troops to NATO's International Security Assistance Force in Afghanistan, behind the United States and Britain.
After the end of combat operations this year, a NATO follow-up mission will take over on January 1st, made up of 9,800 US troops and about 3,000 soldiers from Germany, Italy and other member nations.
The US force will be halved by the end of next year, before being reduced to a normal embassy protection presence by the end of 2016.