This would be the richest contract by total value in NBA history, according to ESPN Stats & Information. It also would be the first deal worth $100 million or more total with an average annual value of more than $30 million per year.
Sources told ESPN that the verbal agreement would be sealed Friday night and the final details were "nearing conclusion."
Conley, 28, who has never been an All-Star and was known for years as the NBA's most underrated player, also met with the Dallas Mavericks on Friday afternoon. However, the Grizzlies were always widely considered the heavy favorites to keep the nine-year veteran, who was drafted by Memphis with the fourth overall pick in 2007.
The Mavs and other suitors could only offer Conley a max contract worth approximately $114 million over four years.
Former Dallas forward Chandler Parsons will be one of Conley's teammates after agreeing to terms on a four-year, $94.8 million max contract with the Grizzlies earlier Friday. Sources said the pair had extended conversations about teaming up with the Grizzlies but never discussed the possibility of playing together in Dallas.
Conley missed 26 games this past season -- the most since his debut in 2007-08 -- including the final 20 with left Achilles tendinitis for a Grizzlies team that made the playoffs despite setting an NBA record for most players used (28) in a single season.
He finished with averages of 15.3 points, 6.1 assists and 2.9 rebounds per game, and had the sixth-best real plus-minus (plus-2.71) among NBA point guards.
The five-year, $45 million extension he signed with the team in 2010 was widely questioned, given his lack of production to that point. But he went on to help lead the Grizzlies to a franchise-record six straight playoff appearances, including a Western Conference finals berth in 2012-13.
During that time, Conley has become a principal figure in the Grizzlies' "Grit 'N' Grind" era. He also has formed a close relationship with center Marc Gasol, and it was widely reported that Conley aggressively recruited his teammate of eight years before Gasol re-signed with the Grizzlies last summer for $110 million over five years.
"Mike [being in Memphis] was big," Gasol told Sports Illustrated this season in regard to his free-agent decision. "I will go through any type of wall for that guy."
Conley was honored with his second Joe Dumars Trophy for sportsmanship this past season, becoming only the third player in the award's two decades to win more than once.
Information from ESPN's Justin Verrier was used in this report.