I have had this before, both with celebrities and regular old people people lol. With celebrities or well-known people, it can be hard to discern between liking them and genuinely having a connection. They have their pictures all over the internet, magazines, TV, etc so someone is bound to recognize them at a deeper level. They've had past lives and they have souls too. With non-famous people I find the connection much more eerie because I don't usually realize the connection until meeting them. And then I'm like @_@ whoah. And it's easier to verify because they feel it too and you can discuss the subject, or try divination together. I agree with Nevermore that it is usually more of a past-life connection than a psychic one. A psychic connection would be like telepathically contacting said person, and they speak back. With well-known people it's easy to fake their voice in your mind, so I'm very iffy about the subject. I once knew a woman who was either extremely spiritually developed, or insane. She had this elaborate spiritual life with a (famous) man she had never met. She insisted that they spoke on a soul level and part of me believed her because, well, why not? It's not like it isn't possible, but it was extremely one-sided. And she seemed very mature about it, not obsessive or weird... everything she said was very matter-of-fact and from a multi-angled perspective. In the end, she left the internet and I have no idea what happened to her but I look back on it as one of the weirdest experiences of my e-life XD
Maybe it's just me, but I feel like celebrities and famous people are categorized differently than non-famous people and their spirituality tends to be over looked. Or just sounds plain weird to say "I knew Justin Timberlake in a past life!" lol, the Prime Minister of Japan's wife claims to have known Tom Cruise in a past life and she is pretty spacey. I love her. Here is an article about it:
I once had a meditation where I spoke with a rather well-known person, and upon departing they gave me a white rose (the whole meditation was extremely symbolic and rather fun XD ) and the petals swirled around all movie-style, and upon waking from the meditation I saw lights and little orb-like things swirling away, much like the petals. I think if we were to meet in the physical, we would bond very easily but it isn't something I am concerned about in the least. That life was that life, this life is this life. I'm happy and very fortunate to have the people I do in my current life :3 with or without a past life connection.
I'm sure that if you are meant to see/meet/be with this person you sense a bond with, that fate will bring you together.