Der Spiegel said U.S. Defence Secretary Ashton Carter had sent a letter asking for a bigger military contribution from Berlin.
Its mission currently includes six Tornado reconnaissance jets, a frigate to protect the French aircraft carrier Charles de Gaulle, refueling aircraft and up to 1,200 troops.
The deployment is a direct response to a French appeal for solidarity after militant attacks in Paris killed 130 people. Germany does not plan to carry out air strikes in Syria.
A German Defence Ministry spokesman confirmed a letter had been received from the United States and its content was under consideration, giving no further details.
Germany has over the last two years shown a growing readiness to commit troops to foreign missions.
Defence Minister Ursula von der Leyen said last week Germany might need bigger armed forces to cope with the more assertive role.
She said an analysis into staffing and the organization of combat forces would report in a couple of months on whether personnel levels were appropriate.
More than 3,000 personnel are currently deployed overseas and the Syria mission will raise that by up to 1,200. Von der Leyen also wants to send 650 troops to Mali to help the French campaign against Islamist militants there.
Germany last year started arming Iraqi Kurds fighting Islamic State.
