Daughter being inappropriate with fiancé

Ok, I need some advice! I really hope this situation is just in my head and there's nothing to it, but tell me what you guys think...I've known my fiancé since grade school, but we reconnected after several years, became engaged, and are expecting our first child together. In the time we hadn't talked, I had a daughter in a previous relationship. She's 10 years old. I've only ever had her around one other man that I was serious with for a little over a yr, besides her father(who chooses to no longer be a part of her life in any way). She absolutely loves my fiancé and I guess he gives her that male father figure attention that she needs, treating her as his own. My concern, however, is that at times it seems like she gets very sexually inappropriate with him-not saying she knows what she's doing but sometimes it seems like she does. She begs him to marry her instead of me, and is constantly on him. She climbs into his lap and tries to put his hands around her waist and says things like "you're mine!" I have even seen her staring at his crotch and trying to touch there when they play around. He of course tries to discourage her, but it doesn't help. Him and I have talked about it on many occasions and both of us are unsure what to do, she literally will not stop. She's 10 yrs old and I am unsure how to even approach her about this. What do I say?? I know this may sound weird, but please if anyone could give me some advice or feedback I would really appreciate it. I don't want this to be an ongoing issue for our family, especially with the baby coming in just a few weeks!