Sutter is still under contract with the Flames after being let go as general manager last season. The Kings asked for permission Sunday, a day before firing Terry Murray.
John Stevens was named interim coach, but general manager Dean Lombardi made it clear on his media call Monday that he was looking at other options.
Lombardi had Sutter as his coach in San Jose, and the two have remained friends.
The Kings started 5-1-1 but had gone 8-11-3 since entering Tuesday, dropping to 12th in the conference standings.
"In every franchise there are different levels of expectations," Lombardi said. "This team came into the season with high expectations."
After the Kings lost their fourth straight game Saturday, a listless 2-1 effort against the visiting Dallas Stars, Lombardi decided the following day to make the change. He flew to Boston on Monday morning and went straight to Murray's hotel room to deliver the news.
"The last homestand was kind of like the end of it," Lombardi said. "There was no one glaring moment, it just builds up."
Pierre LeBrun covers the NHL for ESPN.com. Information from ESPNLosAngeles.com's Dan Arritt and The Associated Press was used in this report.