The sentience of the TARDIS is sort of implied if you are either a considering person or religious or both. As described in the last episode of the 2005 season, the Heart of the TARDIS is a Space-Time Vortex that contains the whole of Space and Time. To consciously experience what the Heart of the Tardis/The Space Time Vortex experiences is to be simultaneously aware of "everything that is, everything that ever was, and everything that ever will be". No matter where and when your body actually is.
You can just call it the Universe - experienced totally all at once. It is an experience, so is it a point of view? If it is a point of view, it's the same point of view ascribed by humans to God/Brahman/Allah etc. "Everything that is, everything that ever was, and everything that ever will be", experienced all at once.
If it's a point of view, then arguably it's a sentience. But that God-like point of view might not be sentient, or a sentient process, in itself, but merely a (very large) state of being, or a type of experience available to other sentiences. So the Heart of the TARDIS might not necessarily have to be sentient.
Then again, since it contains awareness of all the sentient beings in the Universe, well, that's a lot of a different type of sentience of a sort, which one could think of as being available to tap into like a computer data-base.
In a related way, episode 13 of 2005 tells us the main difference between human beings and timelords.