Among the winnowing pool of unrestricted free agents still seeking deals, former Arizona winger Paul Bissonnette has been fielding interest of varying levels from roughly “five to six teams,” his agent said, including the Washington Capitals.

“Right now he’s just looking for a good organization where he can contribute more than he’s been able to, to date, in the last couple years in Phoenix,” Mark Guy said Friday by telephone. “He wants to be in a position where he can compete for a solid fourth-line position and be a great team guy. He wants to be in an organization where there’s a chance to win, as most guys do, and looking forward to showing how hard he’s worked to improve his skill level and skating over the last couple years.”

After handing $12.2 million in average annual value to three free agents – Matt Niskanen, Brooks Orpik and Justin Peters – on July 1, general manager Brian MacLellan was left with roughly $1.1 million in cap space.

So, since Bissonnette’s salary cap hit last season was $737,500, according to CapGeek, bringing aboard the 29-year-old might mean a corresponding move for the Capitals, depending on both his salary demands and Washington’s desires. The Capitals already list nine wingers on their active roster — Evgeny Kuznetsov and Brooks Laich are both tabbed as centers, though at least one is likely to play wing this season — but having Bisonnette would also ensure that 20-year-old Tom Wilson wouldn’t regress into the fourth-line bruiser role he had last season and could play top-nine minutes.

Guy declined comment on Bissonnette’s salary demands, both in value and length. “Each situation is different,” he said. The Capitals do not comment on player negotiations, so it’s unclear exactly how to categorize their interest in Bissonnette. But, at least, they have made contact with his camp.

Over 202 NHL games, mostly with the Coyotes, Bissonnette has carved out a consistent profile. Listed at 6 feet, 4 inches and 216 pounds, he has logged 340 penalty minutes, roughly one-third of his aggregate time on ice (1,071 minutes).

In Bisonnette’s small time-on-ice sample size – he’s never averaged more than 6:04 a game over six seasons – his puck-possession metrics, with a 52.6 Corsi-for in five-on-five situations in 2013-14 and 51.5 percent in the season before that, grade favorably.

As the Arizona Republic wrote in April, though, he’s trying to become more than a fourth-line fighter, after dropping the gloves for a career-low three times last season. What the newspaper described as Bissonnette’s “good-guy attitude” would seem to fall in line with a concerted culture change in Washington, headlined by first-year coach Barry Trotz and, most notably, the $27.5 million spent on the veteran leader Orpik.

Guy went a simpler route when asked what his client wanted in a new team, saying Bissonnette is seeking a situation where he can play “more than two or three minutes a night” after his skating time decreased over each of the past three seasons.

“He understands the process and knows there’s only a limited number of jobs out there, or teams out there, that are looking for players who play his type of role,” Guy said. “We’ve had a lot of good discussions with teams. He’s patient in knowing there’s going to be a right fit for him.”

In an article published Thursday, though, Bisonnette seemed to indicate to the Arizona Republic that his options might be more limited than five or six teams:

Bissonnette, 29, said “things are looking positive” with one team but would consider playing overseas if nothing is resolved by the end of August. “I definitely think I have a lot more hockey in me,” Bissonnette said.

Note: Hershey defenseman Chay Genoway, coming off a 52-game, 14-point season with the Bears, has signed with the KHL’s Dinamo Riga, according to the team’s website. The 27-year-old has only played one career NHL game, with the Wild in 2011-12.

Genoway was one of Washington’s 10 “Group 3” unrestricted free agents this offseason. Of that group, three are headed overseas, four remained in the NHL and three – Julien Brouillette, Dustin Penner and Ryan Stoa — haven’t signed with new teams.