Budenholzer has one year remaining on his contract.
The team may also reportedly fire the 51-year-old if the Bucks advance to the Eastern Conference finals but perform poorly at that stage.
Prior to last summer's disappointing second-round loss to the Miami Heat, the Bucks collapsed in the 2019 Eastern Conference finals, blowing a 2-0 series lead to the eventual title-winning Toronto Raptors.
However, despite Budenholzer's previous issues with making adjustments in the postseason, the organization is reportedly optimistic. The Bucks are 41-24 (.631) overall and 5-1 against the Brooklyn Nets and Philadelphia 76ers.
The Bucks own a 154-63 (.710) record since Budenholzer came on board in 2018. A number of players have enjoyed breakout or resurgent years under his stewardship - chief among them, two-time reigning league MVP Giannis Antetokounmpo.
Others who have seemingly benefited from Budenholzer's arrival include two-time All-Star Khris Middleton and veteran big man Brook Lopez, who's rebranded himself as a key floor-spacing, shot-blocking roleplayer.