The 37-year-old reality star struck up a romance with Younes Bendjima earlier this month, just a week after he split from the 26-year-old British beauty.
And Jourdan - who has a six-year-old son, Riley, from a past relationship - is expected to be ''devastated'' by the news her 23-year-old former lover has moved on so quickly.
A source told The Sun newspaper: ''It's early days for [Kourtney and Younes] but they are enjoying each others' company.
''Younes had a great time with Jourdan but their busy schedules became too much and they decided to call it quits.
''He's told friends that he was the one who ended it.
''He's now quietly sparked a relationship with Kourtney and really fancies her. They aren't ready to go public but there's a real chemistry between them.
''They split just a week before he started to see Kourtney. Jourdan will be devastated by this.''
Kourtney met Younes - who began dating Jourdan in May 2015 - at Paris Fashion Week earlier this month.
The 'Keeping Up With the Kardashians' star has been single since splitting from Scott Disick, the father of her children Mason, six, Penelope, four, and Reign, 22 months, last July after nine years together.
But the former couple have repeatedly been rumoured to be planning to reconcile, though Kourtney recently insisted that won't happen.
She said: ''I mean, I'm so happy that Scott and I are getting along so well and that we're co-parenting, but I think hanging out with Scott without the kids...
''Scott can just take any little thing and run with it and think that like we're getting back together tomorrow.
''Right now, I can't even wrap my head around that idea, there's so much work that would be involved and I'm so not even there yet.''
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