Whilst Khloe said the offer was "really nice", she questioned what would happen when he returned to Los Angeles after basketball season, adding: "You're not getting an apartment so I can stay in your house. That's, like, insane."
To which Tristan replied: "Mi casa, su casa ... You could just live there forever."
However, Khloe quickly shut him down, adding to the basketball star and her former partner: "'Stop it. It's not happening. Oh my god."
Meanwhile, Khloe previously confessed she wished Tristan could have been as good to her in their relationship as he is to her now they're split.
In the short preview clip for the family's E! reality show, which returns in full next month, Khloe can be seen telling her former boyfriend and father of her child, True: "Why couldn't you be that way when we were together?"
Khloe has been living with the basketball player amidst the current coronavirus pandemic so he could spend time with his daughter.
And the reality star is said to be "incredibly happy" with Tristan.
A source said: "Despite Khloe trying to keep their relationship more private, she is very much with Tristan. And she is incredibly happy. They are looking for a house together in LA to start fresh."