The phrase "eager gaze" is correct and usable in written English.
It can be used to describe someone's enthusiastic or intense look, often conveying interest or anticipation.
Example: "She watched the performance with an eager gaze, captivated by every moment."
Alternatives: "enthusiastic look" or "keen stare."
At a demented research institute named for William Morris, eager eyes gaze at a computer that can handle UHL, or "Unit Headline Language".
While I was there, for instance, the Italian national election campaign was in full swing, and the larger-than-life photos of eager politicians gazed down earnestly from every wall space.
TAVAN TOLGOI, Mongolia — "All you need to mine here is a shovel," said an awe-struck Indian investment manager as he stood behind a barrier, along with dozens of international mining industry executives and other eager investors, gazing at the immense coal pit gouged out of the rust-colored earth below.
Satel and Dr. Lilienfeld's polemic ultimately seems a little abrupt and shortsighted to a reader who has watched a world-class philosopher gaze with eager intensity at the brain and find in it an infinite series of mirrored selves.
Her gaze is so eager and engaged that you can't help wanting to take a seat beside this commanding distillation of forward-thinking Southern womanhood.
Sagnier's gaze cools from eager longing to increasingly chilly calculation, as Isabelle finds unexpected depths to her own capacity for skulduggery.
It is a strange thing to feel abashed when Ms. Kay's calm, somewhat abstracted gaze meets your own eager one.
Our eager minds grew senseless and our gazes became fixed in silence to the dark crystal ball in front of us.
Eager to have Mr. Bush fix his gaze north, as well, Ottawa first sent Foreign Affairs Minister John Manley and Defense Minister Arthur Eggleton to meet their American counterparts.
Marnie, on the other hand, is willing and even eager to be an object of the male gaze.
