index.html

<script src="https://unpkg.com/vue"></script>
<script src="https://unpkg.com/vue-router"></script>

<div id="app">
  <h2>{{ count }}</h2>
  <button @click="inc">inc</button>
  <button @click="dec">dec</button>
</div>

index.js

const Foo = { template: '<div>foo</div>' }

const routes = [
  { path: '/foo', component: Foo },
]

const router = new VueRouter({
  routes
})

const HTTPRequest = {}

HTTPRequest.install = (Vue, options) => {
  let http = null
    
  Object.defineProperty(Vue.prototype, '$request', {
    get () {
      return {
        request: (method, url, data, redirects = true) => {
          console.log('request');
        },
        get: (url, data = null, redirects = true) => {
          console.log(this.$router);
        },
      }
    }
  })
}

Vue.use(HTTPRequest)

new Vue({
  el: '#app',
  router,
  data: { count: 0 },
  methods: {
    inc() {
      this.count++
      this.$request.get()
    },
    dec() {
      this.count--
    }
  }
})