In an interview published by the newspaper Oesterreich, Faymann is reported to have said "We cannot pretend that all refugees actually have grounds for asylum. Therefore we must intensify deportations."
With hundreds of thousands of migrants claiming asylum status during the past months, Austria has faced difficulties accommodating the waves of people arriving.
Problems in Greece and other closer countries suggest that tens of thousands more are likely to arrive, especially when winter is past.
While many of the asylum seekers want to move on to Germany, the two countries are said to be working on a proposal for a common European asylum law, which will extend the previous Dublin arrangement to take into account the current situation.
At present, asylum seekers from Iraq, Afghanistan and Syria are generally being accepted, with tens of thousands of migrants from other countries now scheduled for deportation to their homelands.
Fayman believes the situation will "be even more difficult next year."
“At the moment there may be fewer refugees (arriving), but one should not confuse the winter with an improvement in the situation,” Faymann was quoted as saying.
“Therefore we must prepare measures now so that we are not surprised in the spring,” he added. The newspaper did not say what those measures were.
Faymann has threatened some EU nations which he believes are not contributing to help with the refugee crisis by accepting more asylum seekers.
He told the German newspaper "Die Welt" that "whoever ends up with more money out of the EU budget than who pays in should not simply duck [responsibility] over a fair distribution of refugees."
"If the protection of the outer borders works as it should, the next step should be the opportunity for the controlled and regulated arrival of genuine refugees," Faymann added.
Austria has received 85,000 asylum applications this year, an Interior Ministry spokesman said. They expect roughly 95,000 applications this year, more than 1 percent of its population, compared with 28,000 registered in 2014.
Last year, 38 per cent of applications were approved, the spokesman said.