"They're dating — it's been at least a few months," said a source close to the couple. "They've been getting closer recently, and they've been hanging out all the time."
The insider also revealed that the young pair are planning to go public after Kendall's 18th birthday on 3 November. "They have that spark right now — they're just realy feeling each other. They're just not putting it out there yet."
The rapper, 21, recently posted a photo on Instagram of what appears to be him and Kendall, who can be seen making a heart shape in the sky with her hands.
Kendall's sister Kylie, 16, also posted the picture.
Young, who was previously linked to Justin Bieber's ex Jasmine Villegas, is said to have started "falling hard" for Kendall this past summer.
"He's so sweet," the source added. "He kind of reminds you of Chris Brown, but way more charming and really talented. He's been working with a lot of big-time producers and artists recently."
While Kendall isn't shy about sharing most aspects of her life with either the cameras or on social media, she wants to keep this part of her life private for now.
"I'm sure everything they do goes through Kris," the insider said. "It has to be approved or it's pre-planned and well thought out. But I think you'll see a lot more of them soon."
Reps did not respond to requests for a comment, but on Thursday Kendall tweeted a message that read, "Enough with the rumors! I'm single, people," next to a smiley face.
It was revealed last month that Kendall had split from her boyfriend Julian Brooks. The pair had been dating since May 2012 after meeting at Sierra Canyon School. Julian is a footballer at the University of Nebraska.