Long-time Wall Street deal maker Wasserstein signed a deal in December to buy the ailing cultural and entertainment weekly from Primedia for $55m (£30.2m).
The deal, which becomes final on Friday, saw the head of investment bank Lazard beat out rivals and established media executives including America Media Inc and New York Daily News owner Mort Zuckerman.
Wasserstein is now understood to have turned to Brown, the former New Yorker and Vanity Fair editor, offering her a lucrative deal to turn around the loss-making 35-year-old magazine.
If she takes the job, it will be the first magazine role she has taken since she launched Talk magazine in August 1999 at a glitzy New York party. Talk fell victim to the economic downturn and closed in January 2002 after backers Hearst and Miramax pulled the plug.
Wasserstein is understood to be ready to inject cash into the title and move New York Magazine upmarket so it can better compete with The New Yorker.
New York Magazine is long past its heyday in the late 1960s and early 1970s under editor Clay Felker.
Since Talk closed, Brown has picked up a column in the Washington Post and a weekly talk show on US cable channel CNBC called 'Topic A with Tina Brown', which has featured the likes of Whoopi Goldberg, cable magnate Barry Diller, Lord Black and Simon Schama.
Brown is not the only name in the frame. Peter Kaplan, editor of the New York Observer, is also believed to be interested in the job and is reported to be in talks with Wasserstein to replace current editor Caroline Miller.
Wasserstein adds the magazine to his existing media holdings, which include The Deal, a mergers and acquisition weekly and subscription-based website, the American Lawyer Media Group and Real Estate Media.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .