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If confirmed, the mammoth deal will be the richest contract in NBA history, eclipsing the $264 million extension inked by two-time MVP Nikola Jokic last year.
The 26-year-old Brown has been one of the mainstays of the Celtics' success in recent years, helping the team reach the playoffs for seven consecutive seasons.
Brown's new deal will ensure the two-time All Star remains in Boston until the end of the 2028-2029 season.
Brown had one year remaining on his existing deal with the Celtics, which will pay him $31.8 million for the 2023-2024 campaign.
Brown posted career-best figures of 26.6 points, 6.9 rebounds and 3.5 assists per game in 2022-2023, forming a potent offensive partnership with Jayson Tatum.
However, the Celtics' season ended in disappointment with the team losing at home to Miami in game seven of the Eastern Conference finals.