-- What is happening here is so common and natural that Freud discussed it and felt it was actually helpful in successful psychoanalysis. It's called "transference".
It's genuine feelings on your part, but I'm afraid that as a professional he will not be able to return them, or at least not able to act on them.
-- This is also something that you can express without fear of judgement on his part. Any experienced counselor not only has this happen regularly, but are sensitive and understanding and will be able to guide you in exploring why you feel this, what the feelings actually are and how to use this to make even more headway in your therapy.
-- Now, the other reason you need to tell him what you're feeling is because if it's mutual beyond his wanting to work with you, he can make arrangements to provide alternative options for your counseling and free himself up to pursue a private relationship without fear of losing his license or job.
This is a 'win win'. By confiding in him how you feel, you eliminate the doubt or question about it and either have a new relationship, or find out that he prefers to remain professional and can help you work through the transference.
By the way, transference even occurs with same sex. A woman with a woman counselor or a man with a man counselor will very often have intense, deep feelings for the counselor that in some cases can cause the patient to question their sexuality; however, in many of those cases it's more of a matter of the patient feeling they have a 'best friendship' or are 'like siblings' or soul mates with the physician.
So please just trust him enough to share how you feel.