File Photo: A Shell chemical plant is illuminated in Wesseling, near Cologne, Germany, taken on April 6, 2022. AP
"There are only a few states left who have issues, Hungary above all," Robert Habeck told public broadcaster ZDF on Monday night.
"I think we will achieve a breakthrough within the next few days," Habeck said, adding that discussions were "continuing".
A Russian oil embargo in response to the invasion of Ukraine was "within reach," he said.
Brussels initially proposed that most member states halt Russian crude imports over the next six months and refined fuels by the end of the year.
But Hungary has so far refused to back the plan put forward by European Commission President Ursula von der Leyen.
Hungary -- whose populist leader Viktor Orban has been a rare ally of Russian President Vladimir Putin in Europe -- said it could not support the plan "in this form", as it would "completely destroy" the security of its energy supply.
Brussels has offered Hungary, the Czech Republic and Slovakia long grace periods to phase out Russian oil imports but that has not yet convinced Budapest to budge.
Hungary, often the odd one out in EU decision making, has demanded an exemption from the embargo for at least four years and wants 800 million euros ($860 million) in EU funds to re-tool a refinery and boost the capacity of a pipeline to Croatia.
The outbreak of the war in Ukraine has prompted EU states to try and rapidly reduce their dependence on Russian energy imports, including natural gas.