While Carlyle looks to add to his coaching staff, Nonis will be exploring several trade opportunities.
It has been widely speculated that goalie James Reimer, center Nazem Kadri and defensemen Carl Gunnarsson, Cody Franson and Jake Gardiner could be dangled this summer.
On Sunday evening, Sportsnet's Nick Kypreos reported that the team is actively shopping captain Dion Phaneuf, who signed a seven-year, $49 million contract extension earlier in the season.
Citing "independent sources," Kypreos tweeted that Phaneuf is being shopped to teams in the Western Conference.
Phaneuf was often criticized for his performance throughout the season, specifically his questionable defensive capabilities.
Several Western Conference teams were looking to bolster their blueline, including the Dallas Stars, Edmonton Oilers, San Jose Sharks and Colorado Avalanche, though it's unclear if any of these clubs are interested in Phaneuf.
It's also unclear if the Leafs would consider trading Phaneuf to an Eastern Conference team, if the right offer presented itself.
It is also believed that the Leafs may have to pay part of Phaneuf's salary in order to facilitate a trade.
Whether or not Phaneuf is traded this off-season, a number of other moves are expected in Toronto.
Reimer, a pending restricted free agent, is not expected to be back with the Leafs next season, while the futures of pending unrestricted free agents Dave Bolland, Jay McClement, Troy Bodie, Paul Ranger, Mason Raymond and Nikolai Kulemin are all in doubt.