It seems natural to begin a major coaching search by thinking of presumably qualified candidates already living in the area, and former University of Denver coach George Gwozdecky and his successor, Jim Montgomery, would both be popular choices to replace Patrick Roy behind the Avalanche’s bench.

Gwozdecky and Montgomery, however, both said they have not spoken to Avs general manager Joe Sakic about the position and they don’t expect to get that call. Sakic’s search figures to focus on proven head coaches at the NHL or American Hockey League level, and The Post’s Terry Frei suggests a handful of names in this recently published story.

Gwozdecky, 63, who spent two years as a Tampa Bay Lightning assistant after his 19-year stint at DU ended in 2013, is preparing for his second year as head coach and program builder at Valor Christian High School in Highlands Ranch. The private school has plans to build its own ice arena and possibly go national with its hockey program. Gwozdecky is the only person to win NCAA championships as a player, assistant coach and head coach, but he has never been a head coach in the pros.

Montgomery, 47, is preparing for his fourth season at DU after leading the Pioneers to the NCAA Frozen Four in April, their first trip to the national semifinals since Gwozdecky’s 2005 team won the second of two national titles. Montgomery’s first two Denver teams advanced to the NCAA Tournament, losing in the first round and quarterfinals, respectively. Before DU, Montgomery had extraordinary results in North America’s top junior-A league, the United States Hockey League, where he guided the Dubuque Fighting Saints to two Clark Cup championships and a second-round appearance in three years. Montgomery had a long professional playing career but he has not coached at hockey’s highest level.

The Avs have said Sakic won’t comment on his search until it is over.