Despite last-place finish in the Western Conference, Coach Tony Granato will return next season.
Roy will continue to be co-owner, general manager and head coach of the Quebec Remparts in the Quebec Major Junior Hockey League.
The newspaper reported Roy called Avalanche president Pierre Lacroix Tuesday night and said he would not accept for family reasons.
"I felt pretty comfortable moving up, but the family situation is just not quite there for me right now," he told the newspaper Tuesday night. "When it comes to family, it's always easier to make a decision. Don't get me wrong here, I have the Avalanche at heart (and) the door is not closed."
Roy led he Avalanche to Stanley Cup titles in 1996 and 2001 and also won the Cup with Montreal in 1986 and 1993.