The two can also have subtley different meanings. "To keep an eye OUT FOR somebody" can mean you're looking after them, making sure they aren't harmed. "To keep an eye ON somebody" can mean you don't trust the person. If there's someone you don't trust or you think may be trouble in the future, you may say to them "I'm keeping my eye on you".

If are to meet your friend at a crowded bus station you would be keeping an eye out for him.

keep an eye open/out (for something) to watch carefully so that you will notice when someone or something appears: Keep an eye out for rabbits in the field. See here some expressions with the word "eye" - http://www.ldoceonline.com/dictionary/eye_1

keep an eye out - means look for someone/something keep an eye on - means to observe/be aware of what someone/something is doing

keep an eye open/out (for something) to watch carefully so that you will notice when someone or something appears: Keep an eye out for rabbits in the field. See here some expressions with the word "eye" - http://www.ldoceonline.com/dictionary/eye_1