But some residents indicated concern about Menino's health and were divided on whether he should run for a sixth term this fall, The Boston Globe said.
Seventy-four percent of respondents said they approve of Menino, the Globe said, a rating that would likely make the election an easy win. However, 43 percent of respondents said they want him to run for re-election, versus 36 percent who don't.
The poll, conducted for the Globe by the Survey Center at the University, comes at a critical time as many are beginning to gear up for the election.
"If Menino ran again, he would probably win handily, but I think there's a desire among a lot of people to have a new mayor," said Andrew E. Smith, director of the UNH Survey Center.
The Globe said Menino, 70, has suffered a series of medical problems recently, including blood clots, diabetes and an acute respiratory infection.
The poll indicated that 60 percent of respondents said Menino's health was a concern that would influence their vote.
The poll of 440 adults was conducted with telephone interviews from March 20-26, the Globe said. It included calls to both land lines and cellphones and included 337 likely voters. The data have a margin of error of 4.7 percentage points.