According to the poll, conducted by Democratic firm Public Policy Polling (PPP) for the League of Conservation Voters, Shaheen leads Brown by 11 percentage points, taking 52 percent support to his 41 percent support.

Brown has hinted that he might be interested in running for Senate in New Hampshire, where he has a vacation home.

"I don’t think I’m done with politics, but I’m not going to rule out anything right now because I really haven’t thought a heck of a lot about it,” Brown told reporters when asked about a possible New Hampshire bid, according to CNN.

He recently told Fox News that "nothing's off the table, and nothing's on the table."

Brown has traveled to New Hampshire in recent weeks, stopping at enough Republican fundraisers and dinners in New Hampshire that local Republicans have begun to seriously consider the possibility of a Brown run.

In the new PPP poll, however, more than half of respondents, 54 percent, say Brown shouldn't run for senate in the Granite State.

Shaheen, a former governor who was first elected to the Senate in 2008, holds double-digit advantages over all other potential GOP contenders in the PPP poll. 

She leads Chris Sununu, son of former Gov. John H. Sununu, by 14 points, state Sen. Jeb Bradley by 15 points, former Rep. Frank Guinta by 18 points and Manchester Mayor Ted Gatsas by 19 points.

Both Bradley and Guinta have told The Hill they're seriously considering pursuing the GOP nomination for the seat. But going into what would be a contentious primary, neither comes out clearly ahead in the poll. 

Both are seen favorably by about one-third of respondents, and unfavorably by about 45 percent. Nearly a quarter of respondents are still unsure about the two.

No Republican tested is above water in terms of favorability.

Shaheen, for her part, has the approval of 53 percent of respondents, while 39 percent disapprove.

The PPP poll was conducted among 933 New Hampshire voters from April 19-21.