The paper's website, denverpost.com, used confirmation from Roy's brother, Stephane, as the basis for the report.
"They're discussing the final details of an arrangement," Stephane Roy told the Post. "Colorado is going to be very happy. Patrick is looking for a new challenge."
Stephane Roy also said his brother and the Avalanche were talking at Patrick's home in Palm Beach Gardens, Fla.
Stephane Roy first posted on his Facebook page Monday that his younger brother, a four-time Stanley Cup champion and member of the Hockey Hall of Fame, was going to replace Joe Sacco as coach of the Avalanche. However, Stephane removed the posting from his Facebook page Tuesday afternoon.
When reached by the Denver Post, the Avalanche would not confirm any reports regarding their coaching search. The team also said in an email to The Associated Press on Tuesday that it "won't comment on any speculation on this issue."
Sakic said Tuesday during a radio interview on 104.3 FM The Fan that he couldn't confirm whether Patrick Roy was a candidate for the job.
Patrick Roy spent eight of his 19 NHL seasons with the Avs, winning the Stanley Cup in 1996 and 2001. The captain of those teams was Joe Sakic, recently named the team's vice president of hockey operations.
Roy retired in 2003 and has been coach of the Quebec Remparts of the Quebec Major Junior Hockey League since 2005, where he also serves as the club's general manager and is a co-owner. Roy guided the team to a Memorial Cup championship in 2006 and has a 307-128-32 record. This season Quebec had 89 points, fifth-most in the league, and lost in the second round of the playoffs.