To be aware, there's no doubt that the intention must be there. It's actually quite possible to be aware without choosing a particular object to focus on. I suppose that's called "choiceless awareness": choosing to be aware but not what to be aware of, not going to the objects but allowing objects hit the awareness.
Personally I think, to do this effectively, the meditator's mindfulness needs to be sufficiently strong and steady, so that it can pick up objects almost effortlessly as they arise and pass away.
I do not know for sure "choiceless awareness" is in the Pali Canon or taught by the Buddha. I do know, however, that it's a useful meditation tool when the meditator wishes to decrease the intensity of effort/energy (viriya) while keeping up mindfulness (sati).
Sayadaw U Pandita, a well-known meditation teacher in Myanmar was quite uncertain what his western students meant with "choiceless awareness" when he first heard it. Later on, as he learns further about it, he thought it's sampajañña (clear comprehension), as found in Satipa.t.thaana Sutta.