I'm asking a colleague if he can do something. Most probably he can't but in case he has new availabilities I want him to let me know very quickly as it's an urgent demand but I don't know how to put it correctly/politely: If you can and are interested, please let me know quickly. If you can and are interested, let me know very quickly, please. If you can and are interested, please let me know soon.
In my opinion "soon" is not urgent. It allows the other person to interpret what they mean by it. For a procrastinator "soon" might mean several weeks.
I suggest "very quickly", "urgently" or, better still, give a deadline, e.g. "by next Friday"
If you can and are interested, please let me know by tomorrow afternoon at the latest so that I can [meet the course-leaders deadline][organise it in time][respond while the offer is still open].