Volkswagen has sweetened its bid to purchase almost half of sports car maker Porsche AG and is prepared to offer considerably more than 4 billion euros ($5.58 billion), Germany's Der Spiegel reported.

The weekly magazine wrote on Saturday that Wendelin Wiedeking, the chief executive of heavily indebted parent Porsche SE, still considered the amount insufficient in talks over the possible sale of a 49.9 percent stake in its healthy, wholly-owned manufacturer of 911 Carrera coupes.

Wiedeking prefers a rival concept to reduce debt that entails the aid of Sheikh Hamad bin Khalifa al-Thani, ruler of the natural gas-rich Gulf state of Qatar.

Der Spiegel wrote the sheikh has stated his willingness, via an investor agreement, to offer 7 billion euros for both a stake of just over 25 percent in the listed holding and Porsche SE's cash-settled options in VW stock that Wiedeking used to hedge the cost of his failed stealth takeover of VW.

An industry source told Reuters on Saturday the 7 billion euros was a realistic amount.

Separately Spiegel's closest rival Focus reported that Volkswagen was working on a legal concept of how to save the Porsche and Piech families that own Porsche SE some 1 billion euros as part of a sale to VW -- money that otherwise would be lost as tax revenue for the finance ministry.

The news emerged as the rival Porsche and Piech clans get set for a supervisory board meeting on July 23 that should decide on the future of the company.

UNANIMITY IN ADVANCE

German newspapers Frankfurter Allgemeine Zeitung and Stuttgarter Zeitung both reported that because of a contractual agreement between the two factions not to split their votes at board meetings, the families would meet in advance to decide.

Porsche and Volkswagen declined to comment.

Volkswagen reportedly originally bid between 3 billion and 4 billion euros for the stake, in a deal that would reverse the balance of power following Wiedeking's ambitious attempt to acquire 75 percent of VW's voting stock.

In the process, his automotive holding company racked up about 9 billion euros of net debt by the end of January, trying to swallow its much bigger rival Volkswagen before the financial crisis turned the tables on the would-be predator.

Now that its gamble to take over VW has backfired, Porsche is fighting for influence in a potential union with the world's No.3 car company and its stable of brands spanning Bugatti and Lamborghini to the Volkswagen Golf.

(Reporting by Christiaan Hetzner, additional reporting by Hendrik Sackmann and John O'Donnell)