Speculation about the departure of Cohn, who is seen leading the White House's effort on tax reform and is a front-runner to possibly succeed Janet Yellen as head of the US Federal Reserve, came in the wake of President Donald Trump's defense of white nationalist protesters in Charlottesville, Virginia, last week.
"That's seen as negative for the economy and the stock market," Karl Haeling, vice president at Landesbank Baden-Wurttemberg in New York said if Cohn were to quit.
Bonds yields fell on the rumor, reversing an earlier rise. They turned higher again after Jonathan Swan, a reporter at the news website Axios, on Twitter cited a source with direct knowledge as saying a rumor that Cohn is resigning was "100 (percent) false."
A White House official said Cohn "intends to remain in his position."
At 11:16 a.m. (1516 GMT), benchmark 10-year Treasury yield was 2.218 percent, down 0.7 basis point from late on Wednesday. It reached a session low of 2.208 percent in the aftermath of the Cohn rumor.
On Wednesday, Trump dismantled two of his business advisory groups when several chief executives in those groups quit following Trump's remarks in which he blamed weekend violence in Virginia on both the anti-racism activists as well as white nationalists.
The dismantling of the panels shook investor confidence in Trump's ability to enact the promises he made during his presidential campaign, in particular on tax reform.