Loki thought for a moment that perhaps that might be for the best -the Aesir not letting her return. Then she wouldn't be faced with his guilt and shame day in and day out. She could live her life. Find another. He certainly wouldn't blame Sigyn if she did. Certainly no one else in his life had stuck with him through his various troubles. Eventually everyone cast him aside, even his best friend. Hell, even his blood-brother with whom he had been with through so much. It stood to reason that eventually Sigyn would turn him aside as well.
And part of him wanted her to go. So he could suffer alone, take the blame for everything that had gone wrong and just accept his fate. It was his own fault for downfall. He wouldn't drag Sigyn down with him. He didn't say that, though.
“You act as though any of them would grant you aid if that aid was to come here.” It was negative, sure, but it was reality. Loki genuinely thought that the whole of his pantheon -wife aside, would never grant him a kindness again.
He sighed and finally turned his head to look at her. He still avoided her eyes. “There are other places, though, in Midgard and beyond. Other gods. Have you ever met Hermes of Greece? Their King, Zeus, sends him to Asgard from time to time. There are other places I've never been...” He paused. Sigyn was not going to like what he was going to say next, he knew it, but he needed to say it. “You could go there. Away from all this.” Loki tried to wave his hand to indicate the cave, Asgard and beyond, but it was mostly stilled by the bindings. “Start anew...”