In one story, Leela asked the Doctor if the Tardis understood them when they spoke to it, and he replied that the Tardis does generate “a low-intensity telepathic field.”
Possibly a spoiler, so
In the Christmas episode, it was explicitly stated that the Tardis has a link with the Doctor and that’s how the Doctor and his companions can communicate with everything. And they start off being unable to understand the invading aliens, and then start to, and at that point Rose realises that the Doctor is back.
Well, actually Douglas Adams actually did write the rough drafts for a serial in which the Doctor decides to give up the heroic daring-do act, and becomes a hermit / monk on an otherwise deserted world, giving the TARDIS to Romana & K-9 and allowing them to fight the forces of evil. BBC execs nixed the idea as heresy - so Adams wrote “Shada” instead. (And we all know how well that turned out :).)