POLL: Here's who voters want to see moderate the presidential debates
Cooper received the backing of 34% of respondents in the Morning Consult survey, followed by Fox News anchors Megyn Kelly with 25% and Chris Wallace with 22%.
CBS's Bob Schieffer, who has moderated a presidential debate in the past three elections, finished fourth in the poll with 17%.
Cooper's CNN colleague Wolf Blitzer was the fifth choice of respondents, garnering 16%.
Cooper was the favorite of Democrats and independents, with 40% and 41% backing him as their top choice, respectively.
The leading choice of Republicans, as well as Trump backers, was Wallace, who received 34% of GOP voters' support.
The hosts of the major network Sunday shows did not fare as well in the poll, with NBC's Chuck Todd landing 7% support, ABC's George Stephanopoulos receiving 5%, and CBS's John Dickerson garnering 4%.
In 2012, Schieffer, PBS's Jim Lehrer, and CNN's Candy Crowley moderated the presidential debates, while ABC's Martha Raddatz moderated the vice presidential debate.
The Commission on Presidential Debates will likely be naming the moderators after Labor Day.
Respondents were asked to select their top three choices. A total of 2,007 registered voters were polled.