A poll commissioned by the New York Daily News found 60 percent of the city's Democrats said they'd vote for the secretary of state to 25 percent for Cuomo, with 15 percent undecided.
Pollster Doug Schoen, who questioned nearly 400 New York City Democrats, said Cuomo remains "very, very popular."
However, Clinton has "represented New York for two terms in the U.S. Senate, has been a presidential candidate, is the secretary of state and her husband was president of the United States," Schoen said. "I think that explains everything you need to know."
Clinton defeated President Barack Obama by 17 points in the 2008 New York primary, which the News said is decided largely by city Democrats.
Schoen worked for Hillary Clinton's 2000 Senate race and for President Bill Clinton, the News said.
Hillary Clinton has said she won't run for office again.
Cuomo has played down talk of a possible run for the White House, saying he's focused on his current job.