When the princess returned, there was no boyfriend in sight. It didn't matter. Even if Han were interested, he didn't stand a chance with Leia. He'd always known that. A royal family member wouldn't date someone with his colorful background.
Besides if her current relationship didn't work out, the Kid had dibs on her next, right? Luke clearly worshipped the red carpet that Leia walked on.
Yet, suppose the princess finally lost control one day and threw herself at him? Could Han resist her? Probably not. If something happened between them, how would Luke react? It might end their friendship.