It comes ahead of an “informal” meeting of EU leaders in Versailles this Thursday.
According to political correspondent Gavan Reilly, a “draft declaration” between EU member states has been seen by Bloomberg.
He reports that the EU27 “agree to phase out all use of Russian gas and oil”.
Russia is the world’s second top producer of crude oil after Saudi Arabia, and supplies about a third of Europe’s needs.
Meanwhile, around 40 percent of Europe’s gas also comes from Moscow.
On Monday, EU energy ministers met in Brussels to discuss how to break the dependency.
France’s ecological transition minister said: “We have to prepare for all possibilities.
“The EU has sufficient gas and oil stocks to withstand short-term disruption.
“However, there is an issue with long-term supplies.”
Moving away from gas is already part of the bloc’s plan to reach net zero.
European Commission president Ursula Von der Leyen said Saturday evening that the EU should end its “dependency” on Russian energy sources.
She said: “The European Union must get rid of the dependency from Russian oil, gas and coal. For that, we have to diversify the supply, we have to get better at energy efficiency, and we have to massively invest in renewables.”
READ MORE: Putin sparks EU panic as he CUTS main gas pipeline and sends prices soaring to record high
The move saw prices skyrocket, surpassing October records that also came from gas squeezes.
But Gazprom agreed to resume transiting gas from Poland to Germany via the pipeline after demand soared.
European natural gas prices skyrocketed again to a record high above €200 (£165) per megawatt-hour.
Russia has been ramping up its gas deliveries to Europe in recent weeks despite its “full-scale invasion” of Ukraine.