The Bundesliga would be the first of the five major European domestic soccer leagues to resume play after a stoppage which has seen almost all football put on hold around the world since mid-March.
German states are set agree on the restart in a teleconference with Chancellor Angela Merkel scheduled for Wednesday, the sources said. Matches would take place under strict conditions – and with no fans in stadiums.
So far Portugal, Poland and Hungary have given dates for restarting their national leagues, all towards the end of May.
The German Football League (DFL) has submitted a health safety plan for games without spectators which includes regular testing of players but no quarantines for entire squads in cases of positive tests.
However, it says that if a player is infected, decisions on the measures to be taken lie with the local health authorities.
On Monday, the DFL said that it had registered 10 positive cases in a blanket test of 1 724 players and staff at its 36 first and second division clubs.