Ahhh the believer and unbeliever situation. @lucyc I'll start by telling you what happened with me and my wife when we met in college.
My wife was not a believer when we first started seriously talking. But I really enjoyed her company and so this was on my mind too. I didn't know whether to stop talking to her or to continue. Long story short I continued. As a matter of fact she was led to Christ through me. This was a huge blessing.
Now every relationship doesn't happen that way. So I'll say this. If the relationship is unfruitful and harming your relationship with God then definitely pray and think things over. But if the vibes are all good and you really enjoy this person then maybe God will use you to show him the Way.
Thank you so so much. This is really a big relief to know owners am not the only one to have experienced this. You know what I'll do, I'll keep what you have said in mind, and then make sure to follow what my heart is telling me. I believe my heart is God's tool to lead me. Thank you very much, am so pleased.