It is possible to say the following: I will arrive as close / near to noon as possible. But 'near' is possibly better than 'close' in this context. Using the word 'close' with time doesn't work particularly well. Around is better. We also say that the time is 'approaching' noon. The time is 'coming up to' noon.

"Around noon" is better than "Close to noon". Example: I will arrive for lunch around noon.