According to the report, the announcement could come later this week.
Bryant will not travel with the team on a road trip to Oklahoma City and San Antonio, but is instead staying back in Los Angeles to be examined by team doctors.
Bryant played in just six games this season before suffering a fractured lateral tibial plateau in his left knee on Dec. 17. The Lakers originally thought Bryant was going to be out for six weeks, but he hasn't played since.
Before the season, Bryant signed a two-year, $48.5 million extension, keeping him with the team through the 2015-16 season.
The Lakers (22-42) are tied with the Utah Jazz for the worst-record in the Western Conference.
More from Bleacher Report:
Although he has expressed hope the Lakers will reload this summer via free agency, indications are the Lakers will piece together a roster around him again with an eye toward saving their salary-cap space for a rich 2015 free-agent class. Despite Bryant's limited availability, Lakers general manager Mitch Kupchak said last month that no one should question Bryant's ability to play "at a high level" next season.