Jones will receive a non-guaranteed contract, which is essentially a training camp invite, a source confirmed.
Jones, 34, appeared in 33 games for the Los Angeles Clippers last season.
He has familiarity with Nets coach Lionel Hollins from their days in Memphis. Jones also attended Duke, the same college as Brooklyn general manager Billy King.
Jones gives the Nets six players with non-guaranteed contracts. Markel Brown, Donald Sloan, Willie Reed, Ryan Boatright and Quincy Miller are the others. Brooklyn also has 12 players on guaranteed deals.
Jones holds career averages of 5.4 points and 1.7 rebounds in 622 games with Memphis, Sacramento, Denver, Indiana, Atlanta, Dallas and the Clippers.