Wojnarowski says that the deal could be finished by early next week.
Other teams were taking a bid for Davis.
But it seemed like Boston didn't want to give "Big Baby" up.
Davis had averaged seven points and four rebounds last year for the Celtics.
With such additions like Rasheed Wallace, Marquis Daniels, and Shelden Williams, Davis may be another figure in part of this process for the Celtics' off-season.