Per Kevin Acee of the San Diego Union-Tribune, Fowler has stepped down and Peter Seidler will take over as the team's control person.
USA Today's Bob Nightengale noted Epstein "has told friends he'd love to be involved in ownership and has had eyes on San Diego."
On Tuesday, Epstein stepped down as president of baseball operations for the Chicago Cubs. Jed Hoyer, who has been the team's general manager since October 2011, will take over Epstein's role.
Per ESPN's Jeff Passan, Epstein told family and friends in a letter that he plans to sit out the 2020 season with a plan to get back in Major League Baseball at some point.
"I do plan on having a third chapter leading a baseball organization someday, though I do not expect it to be next year," Epstein wrote.
According to Ken Rosenthal and Jayson Stark of The Athletic, Epstein could attempt to form an ownership group "with like-minded people and/or longtime associates, then attempt to purchase a club."
There have been increased rumors that teams with an opening in their front office, including the New York Mets and Philadelphia Phillies, could make a play for Epstein now that he's a free agent.
One executive told Rosenthal and Stark that Epstein is "the obvious name" for both teams.
The New York native, who grew up in Massachusetts, is one of the most highly regarded front-office executives in Major League Baseball. The 46-year-old was the chief architect in building the rosters for the World Series-winning Boston Red Sox in 2004 and 2007 as well as the 2016 Cubs team that ended the franchise's 108-year title drought.
During his nine-year run with the Cubs from 2011-20, the franchise made the playoffs five times.