Griffin notified the team last week that he will not pick up his option for next season.
The Clippers are of the understanding that it will take a five-year deal to keep Griffin, a source told Shelburne.
Complicating the matter however, sources told ESPN's Michael Eaves, is that Griffin may not be ready for the start of the next season and could possibly be out until December due to a toe injury that cut short his postseason.
A separate source told Shelburne the team believes Griffin's toe will be healed and he'll likely be ready for the start of the season.
Griffin suffered an injury to the plantar plate of his right big toe in Game 3 of the Clippers' series against the Jazz. He left the game near the half and 12 hours later, the team announced he was out.
The 6-foot-10 Griffin has been plagued by injuries throughout his career, including during the 2016 playoffs, when he suffered a quad injury in Game 4 of the Clippers' first-round series against the Trail Blazers. He did not return for the remainder of the series, and the Clippers were eventually eliminated in six games.
Griffin will become an unrestricted free agent on July 1.