The company would extend Iger's contract if a deal with Fox were finalized, according to sources.
CNBC's David Faber first reported in November Fox held talks to sell some, but not all, of its assets to Disney.
Sources confirmed this week the companies were close to finalizing terms of the deal.
The deal would include Fox's Nat Geo, Star, regional sports networks, movie studios and stakes in Sky and Hulu, among other properties. It would not include Fox's news and business news divisions, broadcast network or Fox Sports.
Comcast, meanwhile, continues to pursue a deal with Fox, as well, although Fox views Disney's bid as superior, sources told CNBC.
Since taking the helm at Disney in 2005, Iger has overseen the acquisitions of Pixar, Marvel and Lucasfilm, which includes the "Star Wars" franchise. He has held several executive positions with the company during the last two decades.
Shares of Disney closed down 1.6 percent Wednesday.
Reporting by Julia Boorstin and David Faber, writing by Sara Salinas.
Disclosure: Comcast owns CNBC parent NBCUniversal.