Butcher, 22, who was selected by the Avalanche in the fifth round (No. 123) of the 2013 NHL Draft, had 37 points (seven goals, 30 assists) in 43 games for the University of Denver, which won the NCAA championship last season.
A college player has four years to sign with the team that drafts him before he can become an unrestricted free agent on Aug. 16 of that last year.
"We anticipate talking to several teams in the next couple of days," Butcher's agent, Brian Bartlett, told the Las Vegas Review-Journal on Tuesday. "I would think a lot of teams would be interested in a young, puck-moving defenseman. Ultimately, it's about finding the best situation for Will to continue his hockey career."
Butcher has spoken to the Buffalo Sabres, New Jersey Devils and Vegas Golden Knights, The Associated Press reported on Wednesday. The Toronto Maple Leafs, Pittsburgh Penguins, Chicago Blackhawks, Detroit Red Wings and Minnesota Wild also may have interest, The Detroit News reported Tuesday.
"Will's going to be on a number of conference calls Wednesday, and if there's an opportunity that's compelling, we'll pursue it," Bartlett told the Review-Journal. "I think with talking to the teams and visiting a couple of the cities, it will take about a week to get it done."
Forward Alexander Kerfoot and defenseman Connor Clifton, among others, also became free agents.
Kerfoot, 23, was selected by the Devils in the fifth round (No. 150) of the 2012 NHL Draft. He had 45 points (16 goals, 29 assists) in 36 games for Harvard last season, tying for the team lead in scoring.
Clifton, 22, was a fifth-round pick (No. 133) by the Arizona Coyotes in 2013. He had 14 points (seven goals, seven assists) in 39 games with Quinnipiac University last season.
They can sign a two-year, entry-level contract worth $925,000 a season, plus bonuses that can go as high as $2.85 million per season, according to CapFriendly.com.
Forward Jimmy Vesey, who won the Hobey Baker Award in 2016 at Harvard, opted not to sign with the Nashville Predators, who selected him in the third round (No. 66) in 2012, or with the Buffalo Sabres, who acquired him in a trade with Nashville. He became a free agent and signed a two-year contract with the New York Rangers on Aug. 20, 2016.