01chase-mouse.css

.face-outer{
  width: 60%;
  margin: 0 auto;
}
.face-outline{
  position: relative;
  border: 1px solid #333;
  border-radius: 50%;
}
.face-outline::before{
  content: "";
  display: block;
  padding-top: 100%;
}
.face-weye{
  position: absolute;
  top: 25%;
  width: 25%;
  border: 1px solid #333;
  border-radius: 50%;
}
.face-weye::before{
  content: "";
  display: block;
  padding-top: 100%;
}
.face-weye.left{
  left: 16%;
}
.face-weye.right{
  right: 16%;
}
.face-beye{
  position: absolute;
  top: 50%;
  left: 50%;
  width: 20%;
  transform: translate(-50%,-50%);
  background-color: #333;
  border-radius: 50%;
}
.face-beye::before{
  content: "";
  display: block;
  padding-top: 100%;
}
.face-mouth{
  position: absolute;
  left: 50%;
  bottom: 18%;
  width: 50%;
  transform: translateX(-50%);
  border-width: 0 0 1px 0;
  border-style: solid;
  border-color: #333;
  border-radius: 50%;
}
.face-mouth::before{
  content: "";
  display: block;
  padding-top: 50%;
}

02chase-mouse.html

<div class="face-outer">
  <div class="face-outline">
    <div class="face-weye left">
        <div class="face-beye left"></div>
    </div>
    <div class="face-weye right">
      <div class="face-beye right"></div>
    </div>
    <div class="face-mouth"></div>
  </div>
</div>

03chase-mouse.js

const max_d = 200;
const beye = document.getElementsByClassName('face-beye');
const beye_r = beye[0].clientWidth/2;
let eye_pos;
window.addEventListener('load',()=>{
  eye_pos = [...beye].map(el=>{
    const cr = el.getBoundingClientRect();
    return [window.pageXOffset + cr.left + el.clientWidth/2, window.pageYOffset + cr.top + el.clientHeight/2];
  });
  window.addEventListener('mousemove',chase_mouse);
});

function chase_mouse(e){
  const pos_mouse = [e.pageX, e.pageY];
  [...beye].forEach((eye,i)=>{
    let d_eye_mouse = [e.pageX - eye_pos[i][0], e.pageY - eye_pos[i][1]];
    let d = Math.sqrt(Math.pow(d_eye_mouse[0],2)+Math.pow(d_eye_mouse[1],2));
    const cos = d_eye_mouse[0]/d;
    const sin = d_eye_mouse[1]/d;
    if(d>max_d) d=max_d;
    const black_d = (50-100*beye_r/eye.parentElement.clientWidth)*d/max_d;
    eye.style.left = `${50 + black_d*cos}%`;
    eye.style.top = `${50 + black_d*sin}%`;
  });
}