The 29-year-old socialite - who has been dating the Dallas Cowboys player since August - is said to have called time on their relationship before heading to Europe with mum, Kris Jenner.
An insider revealed: "They broke up about a week ago. It's typical after a break for Kim to take some time by herself. When she broke up with Reggie Bush she went to Mexico and now after her break with Miles she went to Europe."
However, friends of the 'Keeping Up With The Kardashians' star haven't ruled out a reconciliation between the pair in the future.
The source added to gossip website RadarOnline.com: "I'm sure they'll be on and off again but at the moment, they are 100 per cent definitely off."
The brunette beauty - who also split from NFL player Reggie Bush earlier in the year - recently admitted that while her family are keen for her to find love with a Hollywood star, she just wants a "normal Armenian boy".
Kim explained: "I'm dating. But I don't like blind dates. My mother is trying to come up with all these names in Hollywood, and I'm like, 'Just get me out of here, I want a normal Armenian boy.' I absolutely love them."