I'm going to ignore my old friend's gestures
Why are you going to ignore your friend's gesture?
I'm busy now I don't have time for that
It is rude to ignore your friend when they reach out. Even if you are busy, you should communicate that with your friend instead of ignoring them.
It's OK for me to ignore him because he's stingy.
There are more constructive ways to deal with his behavior than silence. How will he even know that's why you're ignoring him? It would be better to be direct; it might motivate him to change his behavior.