The New York Times vertical also reported that the 88-year-old owner is in talks with a group to potentially do so.
In the past, Reinsdorf has balked at any talk of selling the team. Reinsdorf purchased his stake in the Sox in 1981 for $20 million, leading the charge to build Guaranteed Rate Field. The team is now estimated to be worth more than $2 billion.
The White Sox are looking to build a new stadium in Chicago's South Loop, but are coming off a historically bad season. They went 41-121 this year, breaking the modern major league record for most losses in a season. They had the majors' worst team batting average at .221 and on-base percentage at .278, and they finished last with 507 runs, 133 homers and 485 RBIs.
Reinsdorf is reportedly shopping the team to a group led by former major leaguer Dave Stewart, according to the Athletic.
ABC7 has reached out to the White Sox for comment and received an email response from their vice president of communications saying, "We are responding with our typical 'not commenting on rumors and speculation.'"
The Associated Press contributed to this report.