The Sunday Times claims Sky is the frontrunner for the Italian company's 1.84m UK subscribers after Carphone Warehouse walked away from its bid. Tiscali has been up for auction since it launched a strategic review in February.
The deal would nearly double Sky's existing 1.79m UK broadband customer base, making it the third largest broadband provider in the country, behind BT and Virgin Media.
Initially, Tiscali was expected to go for £1.3bn, a price that has fallen gradually as the Italian firm continued to lose market share and the economy deteriorated.
Vodafone came close to a deal but made an about turn in June after disputes were raised over the company's value.
Carphone Warehouse is understood to have delivered a £600m bid, which dropped to £450m in September.
A number of companies have previously expressed interest in the takeover, including BT, Swisscom and Italian mobile network Wind.
The deal would mark a distinct change in the corporate strategy of Sky, which is currently offering its broadband service only to existing television customers.
In its third quarter results on Friday, the company reported 164,000 new broadband packages had been sold during the quarter, with about one in five of its 9.07m customers now connected to the internet via Sky.
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