Zuckerman has withdrawn his interest following a last-minute bid for the magazine last week, according to Reuters.
The newswire said the move means Bloomberg is now clear favourite to acquire the 80-year-old magazine.
Zuckerman's decision to walk away comes hot on the heels of private equity firm OpenGate Capital deciding it was also no longer interested.
Other bidders no longer in the running include Platinum Equity, headed by Beverly Hills billionaire Tom Gores.