The Keeping Up With The Kardashians star bumped into the singer-songwriter in Los Angeles last month and then she was seated at the same table as him at yesterday's GQ Men of the Year Awards 2014.
And clearly Sam impressed Kim!
Speaking on BBC Radio 1's Breakfast Show today, she said: "I love him. His voice is just... I've never heard anything like it. I think it's so special and he's such a sweet person.
"I've had the chance to meet him a couple of times recently and he's such a kind person. He's really good. He told me he would be walking into Radio 1 today just as I was walking out so we're missing each other.
"I wish I could [stay to hear him perform]."
'Stay With Me' singer Sam was in the Live Lounge today serenading Fearne Cotton on her 33rd birthday. Lucky Fearne!
Meanwhile, Kim jetted into the UK yesterday with husband Kanye West and their daughter North, one. Kim and Kanye were at last night's GQ Men of the Year Awards 2014 so Kim could accept her 'Woman of the Year' prize.
Reveal is now on Google Plus! Join us here for the latest pictures, fashion and celebrity news!