The process has so far faced obstacles from minority shareholders of Frankfurt-listed Sky Deutschland, the paper said, citing sources.
The deal would create a European pay-TV powerhouse with 20 million subscribers, with analysts giving an acquisition a likely price of 7-10 billion euros (5.5-7.9 billion pounds).
Murdoch's 21st Century Fox owns 100 percent of Sky Italia and 57 percent of Sky Deutschland. Murdoch currently owns a 39 percent stake in BSkyB, the British pay-TV firm.
Both Sky and Fox declined to comment. BSkyB is to report its results on July 25, and is likely to provide more details about the deal then.
Murdoch's empire has a history of bold, if expensive, gambles. Last week 21st Century Fox revealed that its attempts to buy Time Warner had been rejected.
A source put the price of a deal at around $80 billion - which would have made it the 83-year-old magnate's largest-ever takeover.
(Reporting By Freya Berry and Kate Holton, editing by Rosalind Russell)