Wojnarowski and McMenamin added that there are other teams interested in potentially signing Jefferson as well, although Milwaukee already has room on its roster after releasing guard Gerald Green.
The 37-year-old Jefferson would be a logical fit in Milwaukee for several reasons at this stage in his long and successful career.
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Jefferson's last hugely productive campaign came in 2008-09, which was his only season with the Bucks during a previous stint in the organization.
He averaged 19.6 points per game that season and hasn't put up more than 12.3 in a single year since then.
Jefferson is also a former teammate of Bucks head coach Jason Kidd, as they played together for seven seasons with the New Jersey Nets and were key parts of two trips to the NBA Finals.
Perhaps most importantly, R.J. could be a mentor on a young and talented Bucks team that includes rising stars such as Giannis Antetokounmpo, Jabari Parker and reigning NBA Rookie of the Year Malcolm Brogdon.
Jefferson is coming off consecutive trips to the NBA Finals with the Cavs, including a championship in 2015-16.
Last season, Jefferson appeared in 79 games and averaged 5.7 points and 2.6 rebounds per contest, which suggests he could be a solid bench contributor for an up-and-coming Bucks team.