Is it permissible to continue a romantic relationship with a man who is in the process of divorcing his wife, with the aim of confirming his feelings towards me?

It is not permissible for you to speak with this man, correspond with him, or meet him, because that is a cause for falling into what is forbidden. Whoever circles around the protected area is close to falling into it, and Allah's protected area is His prohibitions. If he is serious, then let him propose to you through your guardian. It is not permissible for you to stipulate that he divorce his wife. And your marriage to him is not valid without your guardian's approval.