Leonard swapped Toronto for the Clippers via free agency after leading the Raptors to their first NBA championship in 2018-19.
A return to the Raptors or a move to the Lakers to team up with LeBron James had been mooted for Leonard, who eventually opted for the Clippers after they acquired Paul George from the Oklahoma City Thunder.
Asked how close he was to joining either the Raptors or the Lakers, Leonard told ESPN: "I was very close. Real close.
"When [the Clippers] presented the opportunity of playing with Paul [George], it was easy, it was a yes. I said let's get it going."
Leonard entered free agency coming off one of the best postseason runs ever with the Raptors.
He averaged 30.5 points in the playoffs, was named the Finals MVP and helped the team avoid elimination by knocking down a crazy bouncing buzzer-beater against the Philadelphia 76ers in Game 7 of the Eastern Conference semi-finals.
All-Star Leonard said Clippers head coach Doc Rivers played a role in his decision to join the franchise.
"I grew up a Clippers fan," Leonard said during his introductory news conference on Wednesday. "I loved the Clippers as a kid. With Doc [Rivers] being a championship head coach, that is something I wanted, an experienced coach. And the front office is very transparent with me. They want to win. It's an opportunity for us to build our own [thing] and make history."
George, meanwhile, reportedly asked Oklahoma City to move him to the Clippers, who ended up landing him in exchange for guard Shai Gilgeous-Alexander, forward Danilo Gallinari, five future first-round selections and two pick swaps.
"This [wasn't something] that came out of the blue," George told ESPN. "We were all on the same page. The initial plan was to give it another year, see what we could do, and I did that. We played another year and it felt like we were just stagnant. Next thing was, let's move forward with other plans.
"Again, it was mutual amongst everybody. [The] Thunder got amazing packages out of it ... And we all thought it was a win across the board, we all thought it was the best moment to pull the plug."