When he was showing Simba the kingdom, he said something like "everything the light touches will be yours" meaning that he is the king of everything the light touches. The sun isn't up yet, so he's saying that its Sarabi's time to get him (mainly just because he doesn't want to get up, i think)
As first guest said, Mufasa told Simba (and essentially the viewers) that he is the king of all the light touches. When Sarabi told Mufasa Simba was awake, Mufasa 'disowned' him by saying that BEFORE SUNRISE he is HER SON. Mufasa is not king yet because the sun is not up. He cannot rule over Simba.
i think he just doesn't want to get up at that early hour, so he's like saying that Simba is her son because she has to take care of him at that time. You know kinda like what humans do. Lol -fbg
my mind just exploded