Der Spiegel said authorities were already using their powers under an immigration law introduced this month in conducting an operation dubbed Aktion Kehraus (Action Sweep Out).
The interior ministry declined to comment on the report beyond saying that deportations were a matter for Germany's 16 federal states.
Under new rules, potential deportees will not be able to use normal legal channels to challenge an expulsion order. A special panel of the Federal Administrative Court will be responsible, with no right of appeal.
Der Spiegel said judges were expected to deal with up to 2000 cases a year.
Since the revelations in 2001 that Arab students who had lived for years in Hamburg led the 11 September 2001 attacks on the United States, Germans have questioned their liberal laws under which some suspects even drew welfare benefits.
Interior Minister Otto Schily has suggested that evidence of training at an al-Qaida camp should be clear grounds for expelling a foreign national. Distributing videos calling for "holy war" could also be punished the same way.