Look at him in the last gif. He opens his mouth, and he holds himself back. I bet you, more than anything, that he was going to tell her that he loved her. In this moment, it didn’t matter if it was before he ever met her or if she doesn’t even know him: all he knows is that he never told her those three words. It reminds me so much of the first time on Bad Wolf Bay. Right there and then, he was going to say, “Rose Tyler, I love you," but he ran out of time then. Here, on the deserted and blistery street, he could have said those words, but he held himself back and wasted the opportunity. He ran out of time again. In his tenth incarnation, the Doctor had three chances to tell Rose Tyler he loved her. On Bad Wolf Bay, he was going too. On Bad Wolf Bay the second time, he should have. And here, on New Year’s Day, he couldn’t. This, inevitably, for me, is what cuts him off. It will always be one of his biggest regrets, and one of the reasons why, after he regenerates, he never returns to his previous companions. Sure, the Doctor hardly ever does, but, for Rose Tyler--especially for Rose Tyler—he always came back. She was that important to him. Important enough that, for a split second, he was willing to risk everything in time and space just to tell her he loved her.
However, like many times before, he ran out of time.