Redick, who met with Lakers leadership, including general manager Rob Pelinka, on Saturday, followed up with a Monday phone call with Davis, according to Charania, Amick and Buha.
"The decision to choose Redick came as the Lakers, led by Pelinka, prioritized Davis' voice in the process and ensured that he understood the shared vision," Charania, Amick and Buha wrote.
Redick's reported four-year deal comes over a week after the Lakers made an offer to UConn's Dan Hurley, who rejected the deal in order to stay with the Huskies, per ESPN's Adrian Wojnarowski.
The Athletic reporters added that "other key players" on the Lakers roster also supported Redick's hiring.
Those "other key players" might have included LeBron James, who has co-hosted his Mind the Game podcast with Redick since March but has not yet committed to the $51.4 player option that would keep him in Los Angeles for the 2024-25 season.
Charania, Amick and Buha reported that Redick described his plans for utilizing Davis during his meeting with Pelinka and other Lakers leadership last weekend.
Part of Redick's system will include a focus "on elevating Anthony Davis' involvement, particularly late in games," The Athletic reporters wrote.
That could mean adding center support to the roster and utilizing Davis more at power forward, a position he has told the Lakers he prefers, as ESPN's Dave McMenamin reported last September.
This isn't the first time the Lakers have reportedly weighed Davis' opinion when making a leadership decision.
Sam Amick of The Athletic said on The Rich Eisen Showin May that Davis' relationship with former head coach Darvin Ham was part of the reason the Lakers decided to make a change on the sideline this offseason.
"They know, like everybody else, that AD has a history of having asked for trades in the past ... last thing they wanted was for AD to be frustrated with the situation," Amick said in May.
That motivation may have also contributed to weighing Davis' opinion on the new hire. The Lakers' hopes of returning to title contention center around Davis, who last August signed an extension that will keep him in Los Angeles through the 2027-28 season.
