The New York Times, citing people familiar with the process, said Nooyi has been courted as an administration ally by Ivanka Trump, President Donald Trump's eldest daughter, who is playing a role in the selection of a nominee.
The World Bank's current president, Jim Yong Kim, said earlier this month he would step down from his post in February to join a private infrastructure investment firm. He was first appointed by the Obama administration in 2012 and was reappointed by President Barack Obama in 2016 to serve a second five-year term.
Nooyi, who dined with the president and other business leaders at his Bedminster, N.J. golf club, drew criticism for assuming an advisory role on his business council, which was disbanded after many chief executives quit following Trump's comments blaming "many sides" for white supremacist violence in Charlottesville, Va., in August 2017.
The Times story said that it was unclear whether Nooyi would accept the nomination if chosen by the administration but Ivanka Trump, who has tweeted that she views Nooyi as a "mentor + inspiration," has floated her name as a potential successor.
Nooyi, who joined PepsiCo in 1994, was the food and beverage company's chief executive for 12 years from 2006-2018. She led the company's restructuring, including the 1997 divestiture of Tricon, now Yum! Brands Inc. (YUM) - Get Report .
She also took the lead in the acquisition of Tropicana in 1998, and the merger with Quaker Oats Company, which also brought Gatorade to Pepsi Co. Nooyi was named as the 3rd Most Powerful Woman in Business by Fortune in 2014.
In August, Nooyi issued a statement clarifying her position on the frequency at which public companies should have to report their financial results after President Trump said that one of his tweets was prompted by comments from her. Trump had suggested that he was looking into changing the rules so that publicly traded companies only have to report their financial results every six months, as opposed to every three months as is currently required.
"Many market participants, as well as the Business Roundtable which we are a part of, have been discussing how to better orient corporations to have a more long-term view," Nooyi said. "Most agree that a short-term only view can inhibit long-term strategy, and thus long-term investment and value creation."
Nooyi announced in August 2018 that she would step down as CEO. Ramon Laguarta, the company's president, became the chief executive in October.
PepsiCo did not immediately respond to a request for comment.