"We want to create a media landscape similar to the one in Hungary," Freedom Party (FPOe) leader Heinz-Christian Strache told the woman who claimed that she was the wealthy niece of a Russian oligarch and planned to invest in Austria, in return for political favours.
According to the book by the Sueddeutsche Zeitung newspaper reporters Frederik Obermaier and Bastian Obermayer, the encounter between Strache, senior FPOe official Johann Gudenus and the woman lasted for several hours in a villa on the Spanish island of Ibiza.
Strache said that he and the woman should start talks after her takeover of the newspaper.
"As soon as that is the case, we have to talk openly, we have to stick our heads together," said Strache, who also talked of drawing up a "media concept" for the woman within a few weeks.
He advised her that she could gain even greater control over Austria's media market if she also got hold over a television broadcaster, Strache said.
Soon afterwards, the anti-immigration and eurosceptic politician said that the FPOe could even envisage privatizing one of the channels of state-owned national broadcaster ORF.
Strache also expressed his admiration for Hungarian Prime Minister Viktor Orban and his campaign against civil society philanthropist George Soros.
The media rights group Reporters Without Borders has decried the closure of critical media outlets in Hungary and increasing government pressure under Orban's rule.
The video was recorded several months before Strache became vice chancellor in a coalition led by conservative Sebastian Kurz.
The government collapsed in May in wake of the video, which also showed Strache mulling road and water infrastructure schemes, as well as ways to funnel donations to political parties while avoiding public scrutiny.
However, the book makes it clear that Strache stressed several times that he was not open for corruption and kick-backs, despite the woman's attempts to agree to concrete deals.
However, Gudenus can be heard telling the woman at one point: "It is possible, but he is not saying it, you understand?"
Strache, who has stepped down from all political and party offices, reacted to the book by saying that it exonerated him.
"The book correctly shows that I did not enter into any deal before, during or after that evening," he said in a statement.
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