Sam Amick of The Athletic reported the two sides have agreed to terms with the length of the deal coinciding with general manager Vlade Divac's through the 2022-23 season.
ESPN's Adrian Wojnarowski reported a formal announcement could be made this weekend.
Per Amick, Divac will meet in person with Walton on Saturday.
On Friday, Walton and the Los Angeles Lakers mutually agreed to part ways after Walton failed to reach the playoffs in three seasons as L.A.'s head coach.
After the Kings fired Dave Joerger on Thursday, Walton immediately emerged as a potential candidate to replace him.
Sean Cunningham of ABC10 in Sacramento reported that the Kings' coaching search is moving quickly because Divac knew he wanted to hire Walton, whom he also pursued in 2016. Sacramento turned to Joerger instead when Walton was hired by the Lakers.
Cunningham added that Walton did not consider the Kings three years ago but noted things are different now and that Divac "will land his man."
After a two-year stint as an assistant with the Golden State Warriors that included an NBA championship and a 39-4 record as the interim head coach while Steve Kerr was out after back surgery, Walton joined the Lakers. While the team improved in each of Walton's three seasons in L.A., it never managed to reach the playoffs.
Expectations were high following the signing of LeBron James during the offseason, but James struggled through a groin injury and the roster never properly meshed. The Lakers finished 37-45, which was two games worse than the Kings at 39-43.
Sacramento had its best record since going 44-38 in 2005-06 thanks to the emergence of guards De'Aaron Fox and Buddy Hield. 2018 No. 2 overall pick Marvin Bagley also performed well when healthy, with 14.9 points and 7.6 rebounds per game.
If Walton does land with Sacramento, he will take over a talented team led by the trio of Fox, Hield and Bagley, as well as shooting guard Bogdan Bogdanovic and center Willie Cauley-Stein if he returns as a restricted free agent.
After failing to reach the playoffs as head coach of the Lakers, Walton would be in charge of ending a playoff drought that has lasted for 13 seasons in Sacramento.