Moreover, "she is exactly his type," the source adds.

And Kim apparently had no qualms about introducing her new fellow to the fam: She and Harry dined last night at Dan Tana's in West Hollywood with her dad and stepmom, Rod Stewart and Penny Lancaster; her brother, Sean, and his on-again flame, Adrienne Maloof.

"Kim and Harry sat next to one another" and he was "very cuddly with her," an eyewitness tells E! News. "He had his arm around her." The lad was also seen talking to Kim's pop-icon father for a while as well. 

Sitting this family gathering out, meanwhile, was Kim's 1 1/2-year-old daughter, Delilah, whose dad is Benicio Del Toro.

A rep for One Direction had no comment; a rep Stewart has not yet responded to a request for comment.

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