The Leafs are not expected to re-sign center Tyler Bozak, who is reportedly looking for around $5 million per year on a new long-term contract.
If the Leafs are unable to acquire a center to man their first line, they'll likely pursue Stephen Weiss, who is scheduled to become an unrestricted free agent July 5 and is not expected to re-sign with the Florida Panthers.
Valtteri Filppula could also hit the open market as a UFA if he goes unsigned by the Detroit Red Wings.
However, Nonis has been trying to create several options, including Edmonton Oilers center Sam Gagner.
Gagner has been negotiating a contract extension with the Oilers, but a source close to the situation told TFP "a deal probably won't happen before" July 5.
The Leafs have also been linked to showing interest in Ryan O'Reilly and Paul Stastny of the Colorado Avalanche.