Rivers, who once declared Garnett his favorite player to coach, said he has spoken with Garnett about Minnesota's decision to orchestrate a buyout for the 15-time All-Star, who announced his farewell Friday.
"He doesn't want to play," Rivers said. "I'm sure he won't play again. I think he realized, 'Why am I doing this?'
"I would have absolutely been interested in bringing him here. You always find a place for a guy like that, whose voice in the locker room is so strong, so clear, so impactful.
"He's such a great teacher in practice. He should start a course in leadership. The NBA should designate who the best player is on each team and then they could bring Kevin in and he could teach them how to be the best player and the best leader. Better yet, they could bring him and Tim [Duncan] in and they could teach it together and show people how it can be done in two completely opposite ways."
Garnett was encouraged by friend, confidant and former coach Flip Saunders to sign a two-year, $16 million contract with the Timberwolves in 2015. Saunders envisioned KG as a mentor for the young team he was building, but also planned to include Garnett as a part-owner in a group that Saunders was assembling to buy the team.
Saunders died of Hodgkin lymphoma in October 2015, at the age of 60. Minnesota hired Sam Mitchell, another close Garnett ally, as the interim coach to replace Saunders.
KG, hobbled by knee woes, averaged just 14.2 minutes and 3.2 points per game last season, but became a trusted mentor to Karl-Anthony Towns, the young big man who is the centerpiece of the Timberwolves' rebuilding effort.
"You know how much I'm gonna miss playing with you and just simply having you around,'' Towns wrote on Instagram . "Congrats on having one of the greatest careers the game has ever seen. We talked. I know what I must do. I'll take it from here.''
Moments after the 2015-16 season ended, the Timberwolves fired Mitchell and general manager Milt Newton. Garnett, according to league sources, was visibly upset when told Mitchell would not be retained. His strained relationship with current owner Glen Taylor further deteriorated after Mitchell's ouster.
Taylor acknowledged this week that he hadn't spoken with Garnett for months. Rivers said Garnett's departure from Minnesota was not what he had envisioned, and his ownership opportunity has all but vanished.
"It wasn't a great ending," Rivers said. "I'm not going to say too much about it, but once Flip passed away it threw a wrench into everything."
Rivers said that Garnett feels "really great" and was working out as recently as a couple of weeks ago. His knee issues, Rivers believes, could be handled with the proper regimen of rest and treatment.
"The sad thing is he could play another year if he wanted to," Rivers said. "Maybe that's why he's retired but not retired. He loves the young guys on that Minnesota team. They're great listeners and he loved working with them. It's too bad it's ending like this for him."
Garnett will stay in the game in some capacity, Rivers confirmed, and said he's already thinking up ways to bring him into the Clippers fold. Garnett has a home in Malibu, California.
"I'm going to offer him something," Rivers said. "I don't want to say too much right now. I just know he'd be a great asset to any team."
Garnett, who teamed with Rivers, Paul Pierce and Ray Allen to help the Boston Celtics win the 2008 NBA championship, finishes his career in the top 20 in all-time scoring (17th, 26,071 points), rebounding (ninth, 14,662) and blocked shots (17th, 2,037).
Yet the numbers, Rivers said, don't begin to explain his value.
"Most incredible leader I've ever seen," Rivers said. "He loves the game and played it with a passion you just don't see very often.
"But he's finally had enough. We all get there someday."