I was planning to do a reading project with a professor in my institute and had asked him in the last semester whether it would be possible for me to do it under his guidance. However he had politely denied the request saying that he was a bit busy at that time and maybe we could try it at a later time. Since the semester had ended, I was wondering whether it would be appropriate for me to approach him again with the same request especially as he had told me that he was busy at that time. However, I was wondering whether it would be considered as bad manners as I might be forcing him to reject this for a second time even though he had hinted to me before. Does someone have any experience with this kind of experience and if so could you please help about what is my best course of action?
Yes, it is fine to ask.
However, if you want to increase your chances that he will agree, make it a formal and specific proposal with stated goals. In other words, make it easy for him to say yes and to create criteria for your evaluation. Say what things you will deliver at the end.
That way, even if he is busy, he might just decide that you won't add enough to his work to cause issues elsewhere.
I had two experiences during undergrad where a professor told me they were too busy to supervise a project of mine. In one case I ended up doing a project with that professor later; in the other case I never did.
Since he explicitly said that maybe he could supervise you at a later date, I think it's perfectly appropriate for you to ask again. Just be prepared that he may still be busy.