NEW YORK (Reuters) - New York Police Commissioner Ray Kelly, a popular figure who some Republican backers want to see enter city politics, would be soundly defeated in a mayoral race against any of the three Democrats expected to run next year, a new poll shows.

A Quinnipiac University poll released on Thursday asked voters whether they would support Kelly if he were to decide to run in the 2013 mayoral race as a Republican, even though he has repeatedly insisted he has no plans to enter the contest and isn't registered in any party.

From the look of the poll, that may be a wise decision. It found in a hypothetical matchup against City Council Speaker Christine Quinn - a Democrat and the current front-runner - Kelly trails by 15 percentage points, 48 percent to 33 percent.

He trails by 12 percentage points both former city comptroller and 2009 Democratic candidate William Thompson and Public Advocate Bill de Blasio.

That's not to say Kelly is unpopular. Sixty-six percent of those who responded to the survey approved of the job he is doing as police commissioner, the highest rating of any New York City official. Mayor Michael Bloomberg, who is finishing out his third term, had a 49 percent approval rating.

"Ray Kelly is a great police commissioner and he'd be a good mayor, New Yorkers think - but it's still a Democratic town. All three of the Democrats' top potential candidates beat the popular top cop," Maurice Carroll, director of the Quinnipiac University Polling Institute, said in a statement.

"Voters are taking seriously all that Kelly-for-mayor noise among Republican leaders. More than half think he might run," he added.

Even though Kelly is not registered in any party, the city's Republicans have talked about him as a candidate, pointing to his consistently strong approval numbers and success in driving down crime rates.

Yet Kelly has not been immune to criticism, particularly when it comes to the police department's controversial stop and frisk program. The New York Civil Liberties Union, a prominent rights group, charged this week the program disproportionately targets minorities, particularly young black and Latino men.

Kelly has argued that the department's aggressive efforts to get illegal guns off the street has driven down crime, protected cops, and made criminals think twice about leaving home with illegal guns.

Quinnipiac surveyed 1,066 New York City registered voters from March 3-8. The poll had a margin of error of plus or minus 3 percentage points.

(Reporting by Paul Thomasch; Editing by Eric Walsh)