The European Commission, which draws up sanctions for the bloc, is currently preparing a text that could be put to the 27 member states as early as Wednesday, diplomats said.
Several diplomats said the ban on oil was made possible after a U-turn by Germany, which had said the measure would do too much harm to its economy.
EU foreign policy chief Josep Borrell said Russia was intensifying its attacks in Ukraine, making new sanctions "absolutely essential”.
"We must use our economic and financial abilities to make Russia pay the price for what it’s doing," he said.
The commission will propose introducing the ban over six to eight months to give countries time to diversify their supply, the sources said.
The ban requires unanimous backing and could yet be derailed, with Hungary expected to mount strong opposition as it is dependent on Russian oil and close to the Kremlin.
Other countries are worried that a ban on oil would increase prices at the pump when consumer prices are already sharply on the rise because of the war.
"We must be very attentive to market reactions," one official told AFP on condition of anonymity.
"There are solutions and we will get there in the end, but we must act with great care."
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