A source told Us Weekly that Khloe and Cleveland Cavaliers player Tristan "aren't speaking", while a separate insider said Khloe "has had enough," according to E!.
Kardashian, 34, and Thompson, 27, had been dating for about two years, and Khloe gave birth to the couple's daughter, True, in April last year.
In a now-deleted tweet, Thompson appeared to deny the reports, stating: "fake news", while Woods has so far not commented on the allegations.
Khloe Kardashian arrives at the Kardashian Kollection cocktail party. Photo / Getty
The Instagram star, 21, is close to the Kardashian family and has modelled for Khloe's inclusive-sized fashion label, Good American.
Khloe and Tristan were last photographed publicly together in January, when they were seen leaving Craig's restaurant in West Hollywood.
This is not the first time Thompson has been accused of cheating.
In 2017, he was captured on camera "motor-boating" a woman in a bar and was seen entering a New York hotel with another woman while Khloe was nine months' pregnant.
The fallout — including a tense delivery-room confrontation between Thompson and Khloe's sisters Kim and Kourtney — was documented on camera for the family's E! reality show Keeping Up With The Kardashians.
In an interview with Stellar this month, Khloe said she was trying to keep her personal life private.
Tristan Thompson and Khloe Kardashian attend the Klutch Sports Group. Photo / Getty
"There's not too many things that are secret, I guess," Kardashian said. "I'm so used to being public that it doesn't really bother me. It's just who I am.
"It's my biggest issue — it's hard for me to pull back.
"Everybody doesn't have to know everything. My personal life, my dating life … I've learnt that I want to keep on the private side."
Last May, a source told E! Khloe was giving Tristan "another chance" and was "trying to put the pieces back together for the sake of True".
"Although she is crushed by the scandal, Khloe desperately wants things to work and wants to have a complete family," the source said.
