Capuano, 50, was fired by the Islanders on Jan. 17 after a 17-17-8 start. New York has gone 7-1-2 under Doug Weight since the change.
The Islanders reached 100 points in back-to-back seasons under Capuano, which included their first series win in the Stanley Cup Playoffs since 1993 last season.
"I like him," Golden Knights owner Bill Foley said. "I think he's a real quality family guy. He's a quality coach who the players like to play for and a quality person. (Former Florida Panthers coach) Gerard Gallant is the same way."
Capuano became Islanders coach in Nov. 2010 and was 227-192-64. New York qualified for the playoffs three times with Capuano as coach.
Capuano would have serious competition in Vegas; not only is Gallant available, but the Boston Bruins fired coach Claude Julien on Tuesday, and Ken Hitchcock was fired by the St. Louis Blues on Feb. 1.
"There may be new names to consider, but our main goal hasn't changed," Golden Knights general manager George McPhee said. "We're looking to hire an experienced coach who has had success and who can lead the Golden Knights."
