Asselborn made the remarks at a joint press conference after meeting with his Turkish counterpart Feridun Sinirlioglu on Friday.
"We will not close our doors. We will establish an admission mechanism. The EU member states should receive refugees in an equal way, otherwise we will not be able to handle this case," Xinhua news agency quoted Asselborn as saying.
The EU is currently working on a financial package for Turkey to deal with the refugee crisis, Asselborn said.
After meeting with Asselborn, the Turkish foreign minister held talks with German Foreign Minister Frank-Walter Steinmeier in Ankara.
Turkey and Germany are in full consensus on the refugee crisis, the Turkish foreign minister said. "Germany's attitude should be an example for others in Europe," he said.
The meetings came as the refugee crisis has been escalating, which has seen thousands of Syrians flowing into European states, largely from the Turkish border.
The EU officials will hold a meeting on Tuesday and the European Council will gather to draw up EU's policy on refugees.