No agreement has been reached, but the Bucks and Jefferson, 37, have mutual interest in a possible deal once he clears waivers Monday, league sources said.
Several other teams have expressed interest in Jefferson, league sources told ESPN.
Milwaukee released guard Gerald Green on Saturday, which cleared a roster spot that could be used to sign Jefferson.
Milwaukee is $2.5 million below the luxury tax threshold. Jefferson's minimum veterans's salary is $2.3 million -- with a $1.5 million salary cap hit. If the Bucks claimed Jefferson off waivers, his salary would put the team $5,000 over the luxury tax.
Jefferson has a strong history with Bucks coach Jason Kidd. They played together for seven seasons, including two trips to the NBA Finals, with the Nets. Jefferson has played 16 NBA seasons -- including with the Bucks in 2008-09 -- averaging 12.8 points for his career. He was part of the Cavaliers' 2016 NBA championship team, and he averaged 5.7 points in 20 minutes per game for Cleveland in 2016-17.
Milwaukee has been working to trade several players to clear salary-cap space, including guard Rashad Vaughn and center John Henson, league sources said. The Bucks have been willing to attach a second-round pick in offers for Vaughn, league sources said.