Woman Claiming Tristan Thompson's Her Baby Daddy is Pre-Khloe Hookup

Tristan Thompson did have sex with the woman saying he's her baby daddy, but it was years before she claims, years before her baby was born and long before he began dating Khloe Kardashian ... TMZ has learned.

Sources close to the NBA power forward tell us ... he had a one-night stand with the woman, Kimberly Alexander, sometime during his rookie season in 2011-2012. However, we're told this doesn't line up with her repeated claim he fathered her child ... because the kid in question is between 4 and 5.

After Alexander made the paternity claim, our sources say Tristan confirmed with his legal team he had sexual relations with her but was confident about taking a test because it was impossible for him to be the father based on the timeline.

We're told Tristan and his lawyer, legal pit bull Marty Singer, made it clear ... if Tristan was the dad, he'd gladly pay child support, but he was confident he wasn't, and the DNA test proved his point.

As we reported ... Tristan and Khloe are now threatening to sue Alexander, claiming she's been lying about the kid -- despite Thompson's paternity test proving he's not her child's father -- and defaming Khloe.

Our Khloe sources point out she has no direct ties to the paternity case -- she only got her lawyer involved because Alexander allegedly made false claims about her after Tristan's test came back negative.

We're told Khloe's mindset is it's an issue strictly between Tristan and the woman ... since it occurred years before Khloe and Tristan began dating in August 2016.

Tristan, we're told, thinks it's all just a money grab.