According to the newspaper, such a measure, which was already introduced in the southeastern state of Bavaria, may be taken at the national level if the corresponding decision is made on Tuesday.
Apart from that, German Chancellor Angela Merkel will discuss with the heads of the federal states the introduction of other measures such as the transfer of employees to remote working, Bild added.
Germany's total tally of COVID-19 cases since the start of the outbreak early last year has topped 2 million. The death toll currently stands at 47,622, while some 1.7 million people have recovered.
Austria has already introduced the mandatory wearing of FFP2 face masks. On Sunday, Chancellor Sebastian Kurz said that Austrians would be required to wear it while in public transport and shops starting 25 January.