Embattled former Rep. Anthony Weiner (D-N.Y.) remained stuck in fourth place, with his 10 percent support unchanged from a poll last week.
Polls showed Weiner tied with Quinn for the lead in the primary before he admitted that he continued to send sexually explicit messages to women, well after such behavior drove him from Congress in 2011.
Current Comptroller John Liu finished fifth in the poll with 6 percent support, and former City Council member Sal Albanese had 1 percent. Seven percent of likely Democratic voters were undecided.
With four weeks remaining before the primary, no candidate is polling close to the 40 percent threshold needed to prevent a runoff.
The poll showed that de Blasio would be a significant favorite in a runoff, with a head-to-head lead of 54-38 percent over Quinn, 50-41 over Thompson, and 72-22 over Weiner.
The poll was conducted from August 7-12 and used a sample of 579 likely Democratic voters. The margin of error was 4.1 percentage points.