The phrase "aware of staring" is correct and usable in written English.
It can be used when discussing someone's consciousness or recognition of being looked at or observed by others.
Example: "She was aware of staring from the crowd as she walked onto the stage."
Alternatives: "conscious of being watched" or "mindful of the gaze.".
As a child, I was acutely aware of people staring at me.
On the platform, even those who were aware of the new feature defaulted to the usual method of staring into the tunnel — suggesting that the unconscious rituals of traveling in New York do not easily give way.
We did a campfire cookout and then used the gathering of the natural materials or the calming effect of staring at the flames to teach people about being present and aware of their emotions/reactions.
This man, I became aware, was staring at me - staring, that is, when he was not kissing and nibbling at the nape of a blonde (subsequently identified to me as Eva Marie Saint) beside him.
I rode the train to work, aware of the other passengers staring at my bright red hair.
Agüero was sitting having lunch with Garay and the Newell's left-back Lautaro Formica, talking about shoes, when he became aware of a short kid staring at him.
For years after her facial surgery, she was keenly aware of the changed face staring back at her.
When I was 11, my mother made me aware of how many men were staring at me when we would go places.
At a moment when Americans were growing uncomfortably aware of the way their government was staring at them and storing what they had previously imagined as their private data, consider my soaring sense of my own originality a delusion of my later life.
Her self-deprecating answer: "Elizabeth Taylor, during her heavy period," revealing that she was aware of why people sometimes couldn't stop staring at her, he said.
Be aware, however, that direct staring without blinking may be interpreted as a position of aggression that makes your cat uncomfortable.
