"The Democratic Party has to be totally, 100 percent unified in order to do it," said Capuano. "The bottom line is, yeah, he's a strong candidate by every measure."
Yet Democratic leaders have balked at the idea.
"We will have a very good, hopefully clean, hard-fought primary that will separate the best nominee out of that pack," said state party chairman John Walsh.
Robert Massie, a former lieutenant governor candidate, is already running. Potential challengers include Setti Warren, the first-term mayor of the affluent Boston suburb of Newton; Kim Driscoll, the mayor of Salem; Rep. Stephen Lynch of South Boston; City Year youth program co-founder Alan Khazei; and Robert Pozen, a businessman.
Capuano and Khazei lost the 2009 Democratic primary to replace Kennedy.
"These are middleweights and lightweights," said Dan Payne, a veteran Boston Democratic strategist. "There is a heavyweight, but it is not clear she will run."
That heavyweight is Elizabeth Warren, a Harvard Law professor tapped by President Barack Obama last year to head the Consumer Financial Protection Bureau. She's been dubbed one of "The New Sheriffs of Wall Street" by Time magazine. But she's given no public signs that she is interested in a Senate run.
Ron Kaufman, a longtime GOP strategist, said there's a chance Patrick could eventually decide to run.
"He'll get a lot of pressure from the White House and national Democrats to run," Kaufman said. "They can't keep control of the Senate if they can't pick up a seat in Massachusetts."
Since his surprising January 2010 special election win, Brown has surprised many Democrats with his political savvy. He was an obscure state senator best known for posing nude for Cosmopolitan magazine and campaigning with his pickup truck and his brown leather "barn coat."