Reports of the deal emerged Sunday with the start of the weeklong free agency period. Adrian Wojnarowski of ESPN first reported the deal.
Casspi, 30, can sign the deal on July 6. The Grizzlies will be his seventh NBA team.
The 6-9 forward was waived in April by the Golden State Warriors, where he was under a one-year contract, after suffering an ankle injury. He reportedly is still eligible to receive an NBA championship ring from the team, for which he played 53 games.
Casspi is set to start his 10th season. He has also played for the Sacramento Kings, where he was a No. 1 draft choice, as well as the Cleveland Cavaliers, Houston Rockets, New Orleans Pelicans and Minnesota Timberwolves.
He was a member of the championship Maccabi Tel Aviv team in Israel before making himself available for the NBA draft.