The Red Wings were eliminated from the playoffs in the first round by Tampa Bay, and Babcock's contract expires on June 30. The possibility of his leaving Detroit, where he has coached for the last 10 seasons, has been a hot topic for months as he's highly respected around the league.
Holland said he hopes to have a decision from Babcock by the end of May, and that the Red Wings would be due a third-round pick as compensation from the team that signs him.
Holland said both he and Babcock are headed this weekend to the world hockey championship in the Czech Republic, where officials from many NHL teams are gathered.
TSN's Darren Dreger reported that new Edmonton Oilers GM Peter Chiarelli will reach out to Babcock.
Perhaps eyeing a potential replacement for Babcock, Holland said he would not grant permission to other teams to talk to assistant coach Jeff Blashill.
Babcock, 52, guided the Red Wings to a Stanley Cup win in 2008, and this year helped the team extend its streak of consecutive playoff appearances to 24.
He was also the head coach of the Canadian Olympic teams that won gold in 2010 and 2014.