Attempts to embargo Russian oil failed on Sunday, but the European Union will continue to work on it.
The talks are mostly held up by Hungary, a major user of Russian oil and whose leader has been friendly with Russia's Vladimir Putin.
Hungary, Slovakia and the Czech Republic would be able to continue to receive energy from Russia if the European Commission proposal is adopted. Talks were held up because of demands from Hungary.
The EU's executive arm, the European Commission, declined to comment on the proposals.
Russia is a country that plays an outsized role in global oil markets.
Russia is the third-largest oil producer in the world, behind the US and Saudi Arabia.
Oil prices rose on Monday morning as market participants closely monitored the prospect of the world's largest trading bloc agreeing to impose a ban on Russian oil imports.
International benchmark crude futures were 0.8% higher at $120.41 a barrel.
Since the beginning of the year, energy prices have been high, but have gone up since the beginning of the war against Ukraine.
The EU's sixth sanctions package on Russia would include the proposed sanctions on oil imports.
The previous rounds of measures included restricted access to capital markets, freezing Russia's central bank assets, and banning imports of Russian coal and other commodities.
Talks to impose an oil embargo have been going on since the beginning of the month, but no progress has been made since the European Commission President said member states would ban all Russian oil from Europe.
We are addressing our dependency on Russian oil. Von der Leyen told the European Parliament on May 4 that it would not be easy because some member states are dependent on Russian oil.
The EU’s von der Leyen has said the bloc must address its dependency on Russian oil.It had been hoped that leaders could reach an agreement in time for the summit to show the bloc's unity in the face of the Kremlin. Failure to secure a deal would be seen as a victory for Putin.
Energy-importing countries continue to top up Putin's war chest with oil and gas revenue despite the EU imposing a total embargo on Russian oil and gas.
The analysis shows that Russia's military might is being reinforced by European countries.
Fossil fuels play a central role in the Russian government's budget, as revenue from Russian oil and gas was responsible for roughly 43% of the budget between 2011 and 2020.
Russia is a major producer and exporter of crude oil and refined products, and an embargo on sales would cause significant financial pain.
The EU still finances Russia in the conflict despite the lack of additional measures. Varga said that in the first three months of the war, it acquired energy in the value of $60 billion.
This much the EU admits itself. There is a serious discussion about whether sanctions are the best way to punish Russia or whether tariffs would be more effective.