According to Spiegel Online, dozens of soldiers will be sent to the conflict-ridden area to train Kurdish fighters on mine location and disposal technologies, the news site reported Wednesday evening.
Bild also reported on Thursday that a draft bill shows the parliament hopes to send 100 armed Bundeswehr soldiers to Erbil for further training missions.
The ministers responsible for the bill, Defence Minister Ursula von der Leyen, Foreign Minister Frank-Walter Steinmeier, Interior Minister Thomas de Maizière and Justice Minister Heiko Maas said they would only respond to the reports following Thursday's cabinet meeting in Berlin to discuss the draft.
A source in the Federal Defence Ministry told Bild that in order for the ministers to have their way, there would have to be an amendment to Germany's constitution.
Article 24 permits Germany to join collective security organisations in the name of world peace, meaning there has to be a United Nations (UN) mandate for the Bundeswehr to fight. The UN has yet to issue such a mandate.
In October, the German military sent a €70-million arms shipment to the Kurdish Peshmerga forces in Irbil who are fighting Isis soldiers in the northern Iraq. Several delays hampered the mission. The soldiers sent on the training mission were also delayed when they weren't granted entry permits by the Iraqi government.
The shipment itself was already met with opposition in parliament as Germany's history makes politicians conflict-shy. Until the fight against Isis, Germany refused to send arms to active conflict zones and would instead send humanitarian aid.