A week after Patrick Roy’s surprise resignation as coach, the Avalanche is tightening its focus on a pool of candidates that includes Jared Bednar, head coach of the American Hockey League’s recently renamed Cleveland Monsters.

Other coaches the Avs appear to have interest in looking at, but aren’t necessarily limited to, include Washington Capitals assistant Lane Lambert, New York Rangers associate head coach Scott Arniel and another AHL coach, Travis Green of the Utica Comets.

NHL rules require the Avalanche to receive permission to talk to those four, plus any other coaches under contract, for the upcoming season. Bednar recently signed a two-year extension with the Columbus organization, according to Blue Jackets assistant GM Bill Zito, but AHL coaching contracts usually have out clauses to accept NHL head coaching jobs.

Avalanche spokesman Jean Martineau Thursday said the search was about to enter the preliminary phase of the interview process. The team has said general manager Joe Sakic won’t comment until the search is completed.

Bednar, 44, led the AHL team then known as the Lake Erie Monsters to the Calder Cup championship last spring, his fourth year with the Columbus Blue Jackets organization and second as head coach. He has ties to the Avalanche: Second-year Avalanche assistant general manager Chris MacFarland — who now has major influence in organizational decision-making — formerly held the same position for the Blue Jackets. Also, former Avalanche defenseman Nolan Pratt, one of Bednar’s assistants, joined the Colorado coaching staff as the team’s third assistant last month.

Bednar was a journeyman minor-leaguer in the ECHL, AHL and International Hockey League. He is 81-50-21 in two years with Cleveland and previously had a two-year AHL head-coaching stint with the Peoria Rivermen, where he went 81-66-21. Bednar, from Yorkton, Sask., also coached the South Carolina Stingrays to the ECHL championship in 2008-09.

Lambert, 51, is from Swift Current, Sask., and spent the past five seasons as an NHL assistant with the Nashville Predators (three years) and Capitals (last two). He was a AHL head coach with the Milwaukee Admirals for four seasons, from 2007-11. The Admirals were 178-103-39 in that span and advanced to the playoffs each season.

A center, Lambert played 283 NHL games with Detroit, the New York Rangers and Quebec, and in his final season, he played 13 games with the Nordiques and was a teammate of Sakic, then a baby-faced rookie.

Green, 45, played 15 seasons as a center in the NHL, with five teams, scoring 193 goals in 970 games. He started out in coaching as an assistant with major junior’s Portland Winterhawks and after head coach Mike Johnston was suspended for recruiting violations, was the interim head coach. He guided the Winterhawks to the Western Hockey League championship in 2012-13. In the Memorial Cup final, the Winterhawks fell to Nathan MacKinnon and the Halifax Mooseheads.

He joined Utica after that, and the Comets have gone 120-78-30 under him the past three seasons. He has one year remaining on his contract with the Vancouver organization, but has an NHL out clause, essentially guaranteeing the Canucks would grant approval for teams to speak with him. Green was interviewed for the Anaheim coaching job before the Ducks hired veteran Randy Carlyle.

Arniel, 53, was Columbus head coach for one season and part of a second before being fired in early 2012. The Blue Jackets were 34-35-13 under him in 2010-11 and 11-25-5 the next season before he was let go.

He also spent time in the AHL as a head coach, serving five seasons as head coach with Manitoba and Chicago and going 218-136-42.

Roy didn’t have NHL coaching experience when the Avs hired him in 2013, but he had spent eight seasons coaching major junior’s Quebec Remparts — also serving as co-owner and general manager — before rejoining the Colorado organization.

NHL teams have trended towards hiring head coaches without NHL experience. Tampa Bay’s Jon Cooper and Jeff Blashill of Detroit won AHL championships before joining the NHL within the last four years and Philadelphia’s Dave Hakstol came straight from the University of North Dakota a year ago.

“That’s how it is these days. Who the heck is this guy? Who is that guy? Where did they come from?” said former longtime NHL defenseman Brian Engblom, now a veteran television broadcaster. “Over the last three or four years in particular, there’s a lot of new blood coming into the NHL. A lot — coming out of junior hockey, college hockey or through the ranks of the American Hockey League. They’re new, fresh names and faces with more modern ideas and analytics.”

Colorado hired Bob Hartley in 1998, a year after he led the Hershey Bears to the AHL championship. Hartley’s predecessor, Marc Crawford, joined the Quebec Nordiques straight from the AHL. Tony Granato, then an assistant, had no head-coaching experience at all before succeeding the fired Bob Hartley, and Joe Sacco moved up from the Avalanche’s AHL franchise — then at Cleveland — to succeed Granato in 2009.

Hartley, Colorado’s coach when the Avalanche won the Stanley Cup in 2001, was fired by Calgary after the 2015-16 season, only a year after winning the Jack Adams Award as the league’s coach of the year. Because he has a year remaining on his Calgary contract, the Avs also would have needed to get permission to talk with him. The same would be true for former NHL head coaches Kevin Dineen and Jacques Martin, now assistants at Chicago and Pittsburgh, respectively.