The move would bar the transportation of Russian oil priced above a certain level to countries outside of the European Union.
At the same time, the deal is a softer approach to the EU proposed ban on Russian oil. Many fear that such a ban would cause oil prices to skyrocket, as Russia provides some 10% of the world's oil supplies.
What do we know about the deal?
Diplomats told the Reuters and Associated Press news agencies on Thursday that EU members were inching closer to agreeing to the $60 cap.
Poland has yet to greenlight the cap, both news agencies reported. The country had been pushing to lower the cap as much as possible.
"Still waiting for white smoke from Warsaw," the AP news agency cited an unnamed EU diplomat as saying. Lithuania and Estonia also reportedly joined Poland in rejecting a higher price of $65-70 per barrel.
The agreement could become a written procedure by Friday, should it secure the approval of all 27 EU members.
On Thursday afternoon, Russian Urals crude was trading at around $70 a barrel, Reuters reported. International benchmark Brent meanwhile traded at about $87, AP said.
How would the cap be maintained?
If approved, the cap is scheduled to go into effect on a December 5 deadline. It is meant to replace a harsher, initial EU proposal of banning Russian oil altogether.
The cap is due for review by mid-January and every two months after that, Reuters reported, citing an EU document. The review is meant to assess the cap to adjust to any oil market "turbulences."
The cap would also involve a transitional period of 45 days. It would apply to any vessels carrying Russian crude oil which were loaded before the December 5 deadline.
EU considers plans to cap Russian gas price
The failure of the proposed price cap would bring doom to the global oil supply, threatening astronomical energy prices worldwide. Russian President Vladimir Putin has threatened to retaliate against any nations which implement a price cap.
However, the key shipping and insurance firms worldwide are based in the G7 countries, which makes the implementation of the cap feasible.