"Could it be possible TO speak with you" is technically correct, but "would it be possible to speak with you" would sound more natural. Starting with "could" is awkward because the idea behind it is more like, "could it be possible that aliens exist?" That is, it's like the start of a philosophical question.

Hi Soffy, Perhaps you are trying to sound very polite by starting with "Could it be possible". It may sound unnatural to the native English speaker. Perhaps you can write "May I speak to you?" Hope this helps. Cheers, Lance