Holiday, 30, would join the Bucks in exchange for Eric Bledsoe, George Hill and three first-round picks, ESPN reported.
The trade would also include a pair of pick swaps.
An All-Star in 2013, his final season with the Philadelphia 76ers, Holiday has spent the past seven campaigns with the Pelicans.
The arrival of Holiday could help convince Bucks star Giannis Antetokounmpo to sign a five-year supermax extension valued at between $220million and $250m.
Holiday averaged 19.1 points, 6.7 assists and 4.8 rebounds for the Pelicans during the 2019-20 season.
Among the favourites for the NBA championship last season, the Bucks were stunned by the Miami Heat in the Eastern Conference semi-finals.
The deal for Holiday would seemingly be similar to what the Pelicans received from the Los Angeles Lakers for Anthony Davis last year.
Davis was traded to the Lakers in exchange for Lonzo Ball, Brandon Ingram, Josh Hart and three first-round picks, and the star helped the Lakers win the championship last month.
ESPN also reported the Bucks were landing Sacramento Kings star Bogdan Bogdanovic in a sign-and-trade and Justin James was also joining Milwaukee, with Donte DiVincenzo, Ersan Ilyasova and DJ Wilson heading in the opposite direction.
ESPN reported the Grizzlies were finalising a deal on Monday that would see them trade selections 17 and 51 for the Pels' 10 and 40 as well as a top-10 protected 2022 pick via the Los Angeles Lakers.
Lithuanian center Valanciunas leaves Memphis after two and a half years, having been the team's third scorer in 2020-21 with 17.1 points per game behind Ja Morant (19.1) and Dillon Brooks (17.2).
He also averaged 12.5 rebounds but heads to New Orleans, where he will be expected to create space for Zion Williamson.
It means another offseason of flux for the Pels, who selected Williamson with the first overall pick in 2019 as former number one selection Anthony Davis left for the Lakers.
The team have so far struggled to surround Williamson with the right talent, although he was an All-Star last season with 27.0 points – the eighth-most in the league.
Adams and Bledsoe arrived in 2020 as another star performer departed, this time Jrue Holiday in a four-team trade. Holiday won the title last week with the Milwaukee Bucks.
Adams contributed only 7.6 points per game and struggled to work in tandem with Williamson, while Bledsoe's 12.2 points made for his worst scoring season since 2012-13.
Crucially, the pair were set to count for more than 21 per cent of the Pels' cap in 2021-22.
New Orleans now have the flexibility to make an offer to Lonzo Ball or to eye up other free agents, including linked Toronto Raptors great Kyle Lowry.
The Grizzlies instead take on Adams' $17.1million and Bledsoe's $18.1m, but they do also now get a look at a top-10 pick in a talented draft class.
