The sources, from oil majors and refiners which process crude in Europe, said Saudi state oil company Aramco told them it would supply all requested additional volumes in April, Reuters reported.
Oil prices have halved since the start of the year because demand has been hit by the coronavirus outbreak and after Russia and OPEC failed to reach a new deal on supply cuts.
Moscow refused to support new deeper cuts and Riyadh retaliated by opening its taps and pledging to pump record volumes on to the market.
Saudi Arabia has made a deep cut to its official selling prices for oil. Arab Light and Arab Medium barrels were offered at selling price of $25-28 per barrel on CIF Rotterdam basis, traders said.
Russia's main blend Urals has been offered slightly higher that $30 per barrel on CIF Rotterdam basis, according to Refinitiv Eikon data.
"We are happy with our allocation. The requests for April was confirmed. I look forward to May if prices remain that attractive", a trader with a European oil company involved in the talks told Reuters.
European oil refiners including Total, BP, Eni and SOCAR have all had allocations for additional Saudi crude oil supplies in April confirmed, the sources said.
Saudi Aramco declined to comment. Total, BP, Eni and SOCAR did not immediately respond to requests for comment.
On Thursday, sources said Saudi Arabia started focusing on boosting supplies to traditional buyers of Urals as it is trying to replace Russian oil in refiners' feedstock around the world, from Europe to India.
Brent crude was on track for its worst week since the 2008 financial crisis on Friday as investors fretted over the impact of the virus on demand and the Russian-Saudi price war.