While 58 percent of respondents said they would like the former secretary of state to be the Democratic standard bearer, 11 percent chose Sen. Elizabeth Warren of Massachusetts, 9 percent opted for Vice President Joe Biden and 4 percent went with New York Gov. Andrew Cuomo. No other potential candidate broke 1 percent.
On the Republican side, 11 percent picked Sen. Rand Paul, R-Ky., while New Jersey Gov. Chris Christie and former Govs. Jeb Bush and Mike Huckabee tied with 10 percent. Sen. Ted Cruz, R-Texas, Gov. Scott Walker of Wisconsin and Rep. Paul Ryan, R-Wis., followed with 8 percent each.
The poll also suggested a gender gap among Republicans. While 15 percent of men said they did not know who they wanted as the candidate or had not made up their minds, 25 percent of women did.
In two-way matchups, Clinton was 6 to 9 points ahead of the leading Republicans.
"Former Secretary of State Hillary Clinton takes a ton of heat on wealth, book sales and her legacy at the State Department, but she emerges with no serious Democratic challenger, while the Republican field remains clustered and flustered," said Tim Malloy, assistant director of the Quinnipiac University Poll.
There are no declared candidates for the 2016 presidential race, and early polls can also be misleading. In 1990, very few people outside of Arkansas knew much about the state's governor, future President Bill Clinton.
The poll suggested Clinton could have a problem -- that most people have long since made up their minds about her. Overall, 48 percent of respondents said they have a favorable view, while 43 percent had a negative one.
Those under 50 and women were more likely to approve of Clinton. Republicans tilted strongly against her, Democrats strongly for and independents were slightly in the negative.
Quinnipiac surveyed 1,446 registered voters between June 24 and June 30. The margin of error is 2.6 percentage points for the whole sample and up to 4 points for partisan subgroups.