It’s implied in the novelization when they’re in the hanger as they’re about to leave Naboo that Qui-Gon is well aware of what is going on between Padme and Sabe when they have their “We are brave, your highness” back and forth.
There’s also Qui-Gon’s tongue and cheek moments on Tatooine when he tells Padme “The Queen doesn’t need to know” and “The Queen trusts my judgment, young handmaiden. You should too.”