The Commercial Appeal reported in its Wednesday edition that West will most likely replace Dick Versace and be given full control of the Grizzlies' basketball operations.
An unidentified source for the paper said the 63-year-old West agreed to a deal with the club, with an official announcement expected early next week.
A spokesperson for West, as well as Grizzlies majority owner Michael Heisley, would not comment on the report.
West retired in 2000 after serving the same position with the Los Angeles Lakers, ending four decades with the franchise as one of the premier players and executives.
During his tenure running the Lakers, West was part of several major deals, including the acquisition of Kobe Bryant via a trade for Vlade Divac just after the 1996 Draft, as well as the signing of Shaquille O'Neal.
He joined the LA franchise in 1960 and went on to play the next 14 years, becoming one of the best NBA players of all time. He has been a part of seven NBA titles, one as a player and six more as an executive.
West was inducted into the Basketball Hall of Fame in 1979, and had his Lakers No. 44 jersey retired four years later.
Versace is expected to slide into Billy Knight's vacated spot as the team's general manager. Memphis fired Knight last Thursday night after the team returned from Seattle following the regular season finale, in which the Grizzlies lost 109-94.
The Grizzlies finished their first season in Tennessee with a record of 23-59.
