Yellen, speaking Friday at the central bank's annual summit in Jackson Hole, Wyoming, touted how a regulation revamp following the financial crisis has helped strengthen the system. She said the crisis "demanded action" and said the reforms "have made the system safer."
That, however, is just the opposite of what Trump has been preaching. The president has long bemoaned the handcuffs he sees Dodd-Frank and other reforms have put on banking, and is unlikely to want a Fed chair at odds with his thinking.
"When push comes to shove, would Trump, who put Scott Pruitt in charge of the EPA and Rick Perry in charge of the Energy Department, really keep on someone who defends financial regulation as strongly as Yellen just did?" Paul Ashworth, chief U.S. economist at Capital Economics, said in a note.
The initial reaction among pundits is that Gary Cohn may just have moved to the front of the line. For months, the head of the National Economic Council has been pushed as a likely Yellen successor, and her speech Friday may have cemented the move. Yellen's term expires in February, and Trump has not said whether he will reappoint her.
Cohn and Yellen are of like minds when it comes to low rates, but diverge on regulations.
PredictIt, an online betting site that allows members to "invest" on the outcomes of various events, put Cohn out in front Monday. The current betting line translates to a 28 percent chance that the former Goldman Sachs chief operating officer gets the post, compared to 24 percent for Yellen. Former Fed Governor Kevin Warsh is emerging as a dark horse, with an 18 percent chance that got a boost in Monday wagering.
Warsh's surge is likely because Cohn also didn't do himself any favors over the past few days. In an interview with the Financial Times, he ripped the president for his response to the racial violence in Charlottesville, Virginia. Cohn said he considered resigning.
"The president demands unwavering loyalty [just ask [former FBI director] Jim Comey], and he never forgets a slight. Yet Trump got a smackdown this weekend from Gary Cohn and Janet Yellen," Greg Valliere, chief global strategist at Horizon Investments, said in his daily note Monday. "Yellen's prospects have slipped even further, after her full-throated defense of tough Wall Street regulations and free trade deals."
Yellen, though, didn't say a whole lot new.
On multiple occasions she has stated the importance of tighter regulations, particularly in capital levels and risk-taking. In congressional testimony earlier this year, she also shot down a Trump contention that the new rules have slowed business lending.
Indeed, Nomura economist Lewis Alexander termed the Jackson Hole speech just a "subtle rebuke" of Trump's stance on regulations, and said the remarks made Yellen's reappointment "marginally less likely."
It was the timing, though, that struck many on Wall Street as curious. At a point where she simply could have been an observer at Jackson Hole, she chose to spoke up.
"Maybe she tried decided to get up and say what she wanted to and she doesn't care how it is interpreted," said Christopher Whalen, head of Whalen Global Advisors. "Normally, people who are angling for reappointment tend to be really quiet. She didn't have to say a thing at Jackson Hole. She could have just stayed in the audience. To me this is an indication that she's expecting to serve out her term and go home."
WATCH: Debating the deeper implications of what Yellen said at Jackson Hole.