Kara Swisher is reporting that News Corp. (NWSA) could finalize a deal for the troubled social network by this Thursday, with Golden Gate Capital and Specific Media emerging as the leading bidders. The sale would be for between $20 and $30 million — a far cry from the $580 million News Corp. paid to acquire the company from its venture capitalists in 2005.

Golden Gate is no stranger to technology companies, with a portfolio that includes chipmaker Aeroflex and enterprise software company Infor. But it has never backed a consumer Internet company, and Swisher’s reported price-tag seems a bit on the low side for Golden Gate. The firm currently is investing out of a $5.5 billion fund, and usually seeks to invest between $25 million and $100 million of equity in each portfolio company. Maybe it somehow views MySpace as a platform upon which it could build, but I’ve got good reason to believe that Golden Gate is not as far along on this deal as Swisher thinks it is.

Specific Media, on the other hand, would view MySpace as an add-on acquisition. The Irvine, Calif.-based online advertising network has been around since 1999, and in 2007 raised $100 million from private equity firm Francisco Partners (an occasional rival of Golden Gate). It previously raised VC funding from Enterprise Partners Venture Capital, Kennet Partners and Shepherd Ventures. I assume that Specific would have enough cash on hand to complete the deal without an additional equity infusion, but Francisco could certainly afford the cut another check (it closed on a $2 billion fund in 2009).

Specific also has a bit of history with Jon Miller, News Corp.’s chief digital officer. In October 2010, Specific bought Broadband Enterprises, a video ad network that had raised venture capital from a firm – Velocity Interactive Group – where Miller had briefly been a partner.

I’ve got calls into both Golden Gate and Francisco, and will update this post if they respond (don’t hold your breath).