The 33-year-old reality TV star has been asked to allow their three-year-old son Mason to undergo a paternity test by male model Michael Girgenti, who claims they slept together nine months before he was born while she and Scott, 30, were on a break in March 2009.
But the 'Kourtney & Kim Take Miami' star's attorney has branded the Chicago native's allegations ''preposterous and an outrageous lie'' and insisted Kourtney, who also shares daughter Penelope, nine months, with Scott, never gave Michael her contact details after they briefly met at a photo shoot and never came into contact with him again.
Michael, 26, told InTouch magazine: ''After [Mason] was born, and I saw photos of him, I began to wonder. I would definitely want to acknowledge Mason if he's my kid - the deserves to know his real father.''
This is not the first time the extremely wealthy Kardashian family has been confronted by ''preposterous'' paternity allegations.
Kourtney's younger sister Khloe, 28, has had to regularly deny rumours that their late father Robert Kardashian was not her biological father.
Last month she shared her disgust in relation to the rumours with her fans on Twitter, writing: ''Yes, my father is my father and no my parents aren't getting a divorce. You guys can't believe any of these magazines. It's all bulls**t.
''And even though I don't let these stories get to my head. Imagine you at 15 & someone telling you your father isn't your father.
''EWWWW people disgust me. You're all pathetic.
''Wait. But you're ACTUALLY pathetic. Going after a 15-year-old and telling her father isn't her father. Like WHAT? Are you insane?
''This makes me so mad. And I'm not taking the time to write all this because this hurts me. I'm writing this for the other teens my age.''