Chancellor Olaf Scholz of the Social Democrats (SPD), Economy Minister Robert Habeck of the Greens and Finance Minister Christian Lindner from the fiscally conservative Free Democrats (FDP) have so far failed to reach a compromise.
Scholz, whose public ratings as chancellor have fallen to a record low, is keen to reach an agreement, the people said, pointing to uncertainty over how future industrial projects will be funded and the impact that could have on the economy.
Germany's budget has been thrown into disarray by a November Constitutional Court ruling that Berlin could not redirect 60 billion euros of unused funds from the COVID pandemic to climate transformation projects.
On Saturday, Scholz told the SPD's party conference he was confident a deal would be reached but said there would be no cuts to the welfare state, an area where Lindner wants reform.
SPD delegates backed a call for another suspension of Germany's self-imposed debt brake, which Lindner opposes.
The impasse has fuelled concerns among local and foreign industrial firms over whether Europe's largest economy can stand by its funding pledges for green transformation projects in the steel, chip and tech sectors.
Union leaders on Sunday warned that unless Germany's three-way coalition finds a solution soon, thousands of jobs and several high-profile investment projects would be put at risk, potentially damaging the country's long-term competitiveness.
"Strategic investment decisions for the coming decades are being made now," said Juergen Kerner, deputy head of Germany's most powerful union IG Metall, who also sits on the supervisory boards of Siemens AG and Thyssenkrupp.
"Now is the time to decide whether Germany will remain a strong industrialised country with good jobs. For this to succeed, it needs a capable state that invests in the future."
Lindner said earlier this week that a political agreement on the structure of next year's budget was likely to come in a couple of days.
($1 = 0.9293 euros)
(Writing by Christoph Steitz; Editing by Catherine Evans)
By Andreas Rinke