Babcock, who coached the Red Wings since the 2005–06 season, was hired by Toronto on Wednesday.
After Babcock left, Red Wings general manager Ken Holland said Blashill is the leading candidate to become the next coach, according to the Detroit Free Press.
Blashill was a Red Wings assistant in 2011–12 before becoming the head coach of the AHL's Grand Rapids Griffins, Detroit's top minor league affiliate.
"Yes, I want to be the next head coach of the Detroit Red Wings," Blashill told reporters on Thursday. "An ultimate goal of mine was to become an NHL head coach; obviously, within this organization, it's a great organization to be part of."
The Red Wings went 43–25–14 this season and lost to the Tampa Bay Lightning in the first round of the playoffs.
- Molly Geary