Iverson would become the highest profile player ever to put on a Grizzlies' uniform.
"We anticipate signing him to a contract very soon," Grizzlies general manager Chris Wallace said.
Grizzlies owner Michael Heisley wants Iverson to provide a big-name attraction for a team that struggled to attract fans to the plush FedExForum to watch a young team rebuilding through the draft.
Iverson, the first overall draft pick in 1996 and the league MVP in 2001, can provide valuable minutes and scoring off the bench needed by a franchise that went 24-58 and tied for the fifth-worst record in the NBA last season.
The 34-year-old free agent said on his Twitter feed that he met Monday with Heisley, general manager Chris Wallace and coach Lionel Hollins in Atlanta.
"I feel that they are committed to developing a winner and I know that I can help them to accomplish that. I feel that I can trust them," Iverson tweeted.
Iverson's agent, Leon Rose, did not respond to messages to his cell, office or from e-mail from The Associated Press.
Iverson tweeted earlier Wednesday that "God Chose Memphis as the place that I will continue my career."
Memphis would be the fourth team for Iverson after starting his career in Philadelphia and playing for Denver and Detroit. He has averaged 27.1 points per game through his 13 NBA seasons, but his production dropped to 17.4 points per game in his 54 games after being traded by Denver to Detroit during last season.