Former treasury secretary Timothy Geithner and Sheryl Sandberg, chief operating officer at Facebook, at the Milken Institute Global Conference in Beverly Hills in April 2015. (Mario Anzuoni/Reuters)

Asked if she would join a Hillary Clinton administration, Facebook chief operating officer Sheryl Sandberg said this week that she’s staying put. But that hasn’t allayed concerns among D.C. progressives about Sandberg accepting a Cabinet role if Clinton wins the White House.

Sandberg is a major topic of speculation in Washington, given her ties to the Clintons and the star power she would bring to a role such as Treasury secretary.

As Silicon Valley’s most famous female executive and author of a best-selling book on women’s empowerment, Sandberg would draw attention to Clinton’s policy objectives on supporting women and girls. (Cue the “Lean In” jokes.) Sandberg would also contribute to the historic bona fides of a Clinton presidency: Remember, no woman has ever led the Treasury Department.

Critics are pointing to Sandberg’s close relationship with former Treasury secretary Larry Summers, the Robert Rubin protege and ex-director of the National Economic Council who has worked as a high-dollar consultant to financial firms. Needless to say, he’s persona non grata with progressives who want to limit Wall Street and corporate influence on a potential Clinton administration.

Summers has been a career-long mentor to Sandberg, who served as his chief of staff at Treasury. D.C. readers might remember how she strenuously advocated for him in print and behind the scenes when Summers went up against Janet Yellen in 2013 for the chairmanship of the Federal Reserve. (Yellen won out after progressives rallied against Summers.) This included defending him after his notorious remark about women and science. “Actually, the rest of that speech was fine,” Sandberg told the Huffington Post.

Progressives, according to interviews with movement figures in D.C., are already taking a hard look at controversies surrounding Facebook for clues about how Sandberg could approach economic policy. Their main concern are the strategies Facebook uses to reduce its federal tax bill, including what then-Sen. Carl Levin (D-Mich.) called the stock-option loophole and the sale of its intellectual property to an Irish subsidiary.

“These things speak to her mind-set,” said one progressive leader involved in vetting potential Clinton appointees for the left. “Facebook has a massive ongoing battle with the IRS. It’s hard not to question her leadership there.” A Facebook spokeswoman declined to comment.

Of course, Sandberg’s is just one of several potential Treasury Department names drifting around town. (She’s a routine figure in political gossip, as 2014 reports saying she might run for Senate in California can attest.) But as progressives point out, Clinton’s commitment to appointing as many women to Cabinet positions as men means Sandberg can’t be discounted. The same goes for Lael Brainard, a Federal Reserve board member who is also not a favorite among progressives.

Our advice: Keep an eye out for future Sandberg trips to Capitol Hill, where she is a regular (and warmly welcomed) visitor.