I'm thinking of dropping a friendship I have with a recent close friend of mine.
What led you to wanting to drop a friendship with a close friend you have?
I just get the feeling that he doesn't care for me anymore.
People loose interest in some friends over time so you would not be alone on this thought process, it is a common occurence. However, good friends are hard to find so you could do some things like ask how they are and be of help to them. That way you don't have to be lacking one friend.
I just want to try dropping him. We will see what happens.
You should do what you can to make it work. I am sure he cares about you and you two can work things out.