BERLIN (Reuters) - Volkswagen has reached a deal with U.S. authorities to settle the case over its cheating of diesel emissions tests that would involve it paying each affected customer $5,000, Germany’s Die Welt newspaper reported on Wednesday.

A logo of Volkswagen is pictured on the wall at the 86th International Motor Show in Geneva, Switzerland, March 1, 2016. REUTERS/Denis Balibouse

Citing unidentified sources close to the negotiations, Die Welt said the agreement would be presented on Thursday to Judge Charles Breyer in San Francisco, avoiding a trial.

Volkswagen (VW) declined to comment.

Earlier on Wednesday, the possibility of a settlement had boosted the carmaker’s shares by 6.6 percent, the biggest gain in Germany’s benchmark DAX index.

A U.S. federal judge last month gave VW and regulators until Thursday to agree on a fix for nearly 600,000 diesel cars on U.S. roads implicated by VW’s emissions test-rigging scandal.

The company does “not believe any expedited hearing or bench trial is appropriate or required”, according to the agenda for the hearing on Thursday at the San Francisco district court about VW’s progress toward reaching a deal with the U.S. Environmental Protection Agency (EPA).

The plaintiffs - a committee representing thousands of consumers who say they were tricked into buying polluting diesel vehicles - proposed an expedited hearing or bench trial, or an expedited “all issues” trial including punitive damages.

Die Welt said the agreement did not include a detailed plan to fix the affected cars, nor were details fixed on fines and other compensation measures, with one source saying the deal would be fleshed out in the coming months.

However, the owners of affected cars should receive $5,000 each in compensation and VW will separately have to pay to fix their vehicles, the paper said.

German lawyer Christopher Rother told Die Welt that plaintiffs in Europe would seek to emulate the U.S. deal for their customers too.

Earlier on Wednesday, two sources familiar with the matter told Reuters that VW would substantially increase the amount of money set aside to cover its emissions test cheating scandal from the 6.7 billion euros ($7.6 billion) currently earmarked.

Europe’s biggest carmaker will make provisions for a double-digit billion-euro amount in its 2015 results on April 28, the sources said, speaking on condition of anonymity due to the sensitivity of the matter.

One said the German company might not pay a dividend to shareholders on the results and if it did, it would be less than 1 euro per share. Volkswagen (VW) paid out 4.80 euros per common share and 4.86 euros per preference share on 2014 results.

VW declined to comment.

The company is struggling to put a cost on the biggest business scandal in its history seven months after it admitted to cheating U.S. diesel emissions tests, as it is embroiled in legal proceedings around the world.

Arndt Ellinghorst, an analyst at market research firm Evercore ISI, expects VW’s total costs from the “dieselgate” scandal to reach about 30 billion euros.

Final provisions will depend on the outcome of talks with U.S. regulators, the Justice Department and the Federal Trade Commission, one of the sources said.

Analysts have said a deal with U.S. authorities, also on financial penalties, would remove a major deterrent to investing in VW, whose shares have lost billions in value since the scandal broke in September.

“It would be a major positive trigger for the stock if VW quantified the total potential cost of the diesel affair,” said Evercore ISI’s Ellinghorst, who recommends buying VW shares.

Scandal-related expenses could cut VW’s fourth-quarter operating profit 70 percent to 992 million euros, a Reuters poll of analysts found.