The 31-year-old blue-liner could give the club needed depth on defence.
Polak is coming off a gruesome leg injury during last spring’s playoffs with Toronto.
The Czech recorded four goals and seven assists in 75 regular-season games in 2016-17.
He became an unrestricted free agent July 31.
Known as PTOs, professional tryouts come with no job security but give players with no contract a chance to prove they deserve one.
The Maple Leafs made the announcement as they kicked off training camp Thursday morning.
In other news, head coach Mike Babcock said the team would once again not have a captain. The spot has been vacant since Dion Phaneuf‘s departure in February 2016.