The Rome-based club was placed on the market last month by its majority shareholder Cirio.
Now, according to reports in Italy, Murdoch is set to hold talks this week with Cirio chiefs over a possible takeover.
According to the Gazzetta dello Sport, the club is looking to secure EUR150m ($149m) from any sale.
The son of Libyan leader Colonel Gaddafi had initially been linked to the club through the Libyan Arab Foreign Investment Company, which already has a 7.5 percent share in rival club Juventus.
However, Al-Saadi Gaddafi has since said he is not interested in acquiring the shares.
Despite its strong brand name, in its latest quarter results, a spiralling wage bill and no Champions League action saw Lazio's club profits drop between July and September, with profit falling to EUR3.6m ($3.62m) - compared to EUR30.1m ($30.21m) 12 months before.
Turnover fell from EUR34.6m ($34.72m) to EUR21m ($21.07m).
