Leonard, who has been hobbled at certain points of the post season, discussed how an injury can affect a National Basketball Association player's game.
But, in May 2017, "unbeknownst to Leonard and without his consent", Nike filed an application for copyright registration of the logo.
The lawsuit, obtained by KSAT-12, claims Leonard designed and authored the logo before he signed with Nike. The ring and pinky fingers of the logo are shaped into a "K", the middle finger and thumb form an "L" and the index finger is created to resemble an elongated "2" - all nods to his initials and jersey number.
Nike is said to have blocked his attempts to use the design. He alleges Nike responded in March saying it owned "all intellectual property rights" to the logo and demanded Leonard stop using it immediately.
Leonard is hoping to regain control of his logo to use it for clothing collections, sneakers, sports camps, and charity events, while New Balance - the company Kawhi signed with following his time at Jordan Brand - would seemingly also be permitted to utilize the graphic. Leonard is scheduled to speak with reporters on Tuesday when practice resumes at the NBA Finals.
A Nike spokesman declined to comment Monday, saying the company does not discuss pending litigation.
The suit claims Leonard then allowed Nike to use the logo on Leonard clothing, apparel and footwear after he signed an endorsement deal with the company on October 26, 2011. The series resumes on Thursday (AEST) at Golden State.