The Austrian Health Ministry told the APA news agency that it was planning a ban, but details on when it will come into force and how low it will last for are yet to be announced.
Belgium similarly announced a ban on all flights and trains from the UK.
The Netherlands were the first country to announce such a ban. The Dutch ban, from 6:00 am (0500 GMT) on Sunday until January 1, came hours after Britain announced a stay at home order for part of the country to slow the new variant, which British Health Secretary Matt Hancock said was “out of control”.
Following the example of the Netherlands, where a ban on all passenger flights from the UK came into effect on Sunday, the German government was considering a similar move as “a serious option” for flights from both Britain and South Africa, the source said.
In Germany, however, the new strain of the virus has not been detected so far, according to the chief virologist at Berlin's Charite hospital, Christian Drosten, on Twitter.
A health ministry spokesman said the government in Berlin was monitoring developments in Britain very closely and working at “high pressure” to evaluate the new information and data regarding the new strain.
Germany was in touch with its European partners, the spokesman said.