Mobile vaccination teams will be sent into care and nursing homes to offer Pfizer/BioNTech or Moderna booster shots to residents, regardless of which vaccine they had originally, says the document.
Doctors will also be able to administer the booster jab to those who qualify, such as the elderly and people with weakened immune systems.
The text justifies the initiative by citing recent studies showing that protection from infection declines with time, putting vulnerable people at risk again.
Although Germany is currently enjoying relatively low infection rates compared with neighbouring countries, case numbers have been creeping up in recent weeks mainly because of the more contagious Delta variant.
There are also concerns about a slowdown in the country's vaccination rate, with just over 52 percent of the population fully jabbed.
- 'Safe return' to school -
In an effort to get more younger people vaccinated, health ministers want to widen access by opening all the country's vaccination centres to 12- to 17-year olds.
Schools and universities should also offer the jabs, the draft resolution says.
Germany's STIKO vaccine commission disappointed many in June when it officially recommended the vaccine only for 12-17 year olds if they had pre-existing conditions, or lived with people at high risk from Covid.
Although adolescents who don't fall into those categories are still allowed to get vaccinated, in consultation with their parents and doctors, the cautious STIKO guidance has slowed take-up.
Within the European Union, the European Medicines Agency has approved the Pfizer/BioNTech and Moderna shots for all over-12s.
Health Minister Spahn tweeted on Saturday that so far one in five of Germany's 12-17 year olds had received their first coronavirus shot.
"There's enough vaccine for all age groups: anyone who wants to, can get vaccinated," he wrote.
If Spahn and his regional peers sign off on the draft text, their decision to encourage all adolescents to roll up their sleeves would essentially see them bypass STIKO, which has said it needs more data before issuing a more general recommendation.
According to the draft, getting children and teenagers vaccinated could "contribute significantly to a safe return to classrooms after the summer holidays".
Germany's Robert Koch health institute reported 2,097 new daily coronavirus cases on Sunday and one death.
Since the pandemic started, Germany has recorded more than 3.7 million cases and 91,659 deaths.
