Hearst is understood to be eager to sell its stake in the US magazine, which it owns with Harvey Weinstein and Miramax Films.
Talks are reported to be at an advanced stage to bring in Lord Black as an investor in the two-year-old magazine, which is thought to be at least three years away from profitability.
The investment follows the recent announcement that Lord Black is to join a group of investors to launch a New York broadsheet, the New York Sun Times.
This would be Lord Black's latest effort to spread his media empire to New York. As well as the New York Sun Times, he previously tried to buy the Daily News in 1992. More recently, he tried to buy the weekly New York Observer with a view to turning it into a Monday-to-Friday daily.
Speculation about the sale follows reports that Hearst was "re-evaluating the relationship" with Talk.
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