Is it suitable to discuss with several professors which of them would be best to supervise me? Quite simply, I have contacted several professors in the same department, and they have all expressed an interest in supervision, and several of them have also said, &quot;you should also consider professors X, Y...&quot; So I ask:
Can I disclose in my correspondences that &quot;yes, I am also in discussions with professors X, Y...&quot;? I feel like the scenario is a bit like being in Dragon's Den and I don't know whether it would be a good idea and then have them potentially discussing me behind my back? Or what does happen in these circumstances usually?
Yes, you can do that. You are taking their advice, actually, and giving them information they might want. But don't neglect to also say that you are (very) interested in either working with them or keeping contact.
But it is also essential that you have a conversation with each of them about how it will play out if you become their student. You want to know if they have good research ideas (in case you aren't yet committed) and that they will be able to spend sufficient effort on your behalf.
It is also useful to speak with  one or more of their current students to get feedback on such things.