A group of EU member countries, including Germany, want to extend border controls in the Schengen free-travel zone, as the number of refugees fleeing from war and poverty show little sign of decrease, the Welt am Sonntag newspaper reported.
Austria, Belgium, Sweden and Denmark are the countries that are pushing for an extension of border checks.
EU interior ministers will discuss the initiative on Monday, the newspaper added.
Germany has already increased its border controls until May and if the extension push is approved, it will prolong it until the end of 2017.
Over one million refugees arrived Europe in 2015, many coming in through Greece.
Earlier on Saturday, Austrian Interior Minister Johanna Mikl-Leitner warned Greece with "temporary exclusion" from the Schengen zone.
"If the Athens government does not finally do more to secure the [EU's] external borders then one must openly discuss Greece's temporary exclusion from the Schengen zone," she told the German daily Die Welt.
"It is a myth that the Greco [Greek]-Turkish border cannot be controlled," she said.
European leaders who met at the World Economic Forum in Davos, Sweden, warned that the EU could unravel if member states fail to agree on a common approach to the refugee crisis and challenge security in the next few months
When asked if the refugee crisis risks Schengen, the International Monetary Fund (IMF) Chief Christine Lagarde said "Yes, I think so."
"The refugee crisis is a bit of a make or break, from my personal perspective," Lagarde said.