For general manager Jon Horst, Budenholzer was long his top target and a finalized contract is expected to be completed soon, league sources said.
The other finalist for the job, San Antonio assistant Ettore Messina, was informed that he was out of the running on Wednesday, league sources said.
Budenholzer, who parted ways with Atlanta last month, met with Bucks ownership on Tuesday in New York.
The Bucks wanted to have the two players — especially Antetokounmpo, the franchise star — to have a sense of the prospective next Bucks coach and encouraged the players to sit-down with Milwaukee’s preferred candidate before the organization extended a formal offer, league sources said.
It is a relatively unprecedented move in a head coaching search, but it clearly reflects the Bucks determination to make Antetokounmpo and Middleton feel a part of the process.
Budenholzer flew to Milwaukee for the Wednesday morning meeting with the Bucks players. Messina could still be summoned to Milwaukee for a meeting with the players too, league sources said, but that will largely be determined on the Bucks next step with Budenholzer.
Toronto met with Budenholzer on Monday, but never extended an offer, league sources said.
Budenholzer and the Atlanta Hawks parted ways in April, after the two sides could no longer see a path together with the franchise’s rebuilding plans and new management structure.
Before the split, the Hawks gave Budenholzer permission to speak with the Phoenix Suns and New York Knicks for their coaching openings. He pulled out of contention for the Suns job after several conversations with ownership and management.
Considered one of the NBA’s best tacticians. Budenholzer had been the Hawks president of basketball operations — until surrendering front office control with the arrival of GM Travis Schlenk in the spring of 2017.
Budenholzer won his coach of the year award after a 60-victory regular season and a trip to the Eastern Conference Finals in 2016. The Hawks reached the playoffs in four of his first five season. Atlanta dropped to 24-58 this season, with the organization’s mandate to shed salary and gather draft picks and future assets.
Budenholzer spent 17 years as an assistant under Spurs coach Gregg Popovich before his hiring in Atlanta in 2013. He won four NBA titles as a member of Spurs’ staff.