Johnson is scheduled to earn $2.8 million in 2012-13, the final year of his current contract.
He averaged 9.1 points, 4.7 rebounds, 1.1 steals and 1.4 blocks per game last season, but is no longer in Toronto's plans after the recent arrival of Landry Fields and Linas Kleiza's return to health.
Johnson was drafted 16th overall by the Chicago Bulls in 2009. He was traded to Toronto during his second season.
The Raptors, meanwhile, continue to search for a new home for veteran point guard Jose Calderon. ESPN.com reported Thursday that the Raptors and Calderon's representatives were working on a trade together in the wake of Toronto's recent acquisition of Kyle Lowry to be the starter.
The Raptors have let it be known that they prefer not to release Calderon through the NBA's amnesty clause, which is only an option through Tuesday, until next summer's one-week amnesty window in July 2013.
"We have had a few more trade inquiries regarding Jose, (but) the scenario doesn't seem to present itself to a trade today," Raptors president and general manager Bryan Colangelo told the Toronto Sun at the summer league in Las Vegas. "But we'll continue to monitor that and just try to determine whether it's going to work in the long run."
As for making use of the amnesty clause before Tuesday night's deadline, Colangelo told the Sun that he doesn't "anticipate doing something with amnesty, but until the deadline passes, you never want to close that door."
Information from The Associated Press was used in this report.