component.vue

<template>
  <div>
    <select v-model="selected_hour">
      <option v-for="(value, key) in hours" :value="value">{{ value }}</option>
    </select>
  </div>
</template>

<script>
export defaul {
  data () {
    return {
      selected_hour: '9:45'
    }
  },
  computed: {
    hours () {
      let arr = [], i, j;
        for(i=0; i<24; i++) {
            for(j=0; j<4; j++) {
                arr.push(i + ":" + (j===0 ? "00" : 15*j) );
            }
        }
        let d = new Date(),
            h = d.getHours(),
            m = 15 * Math.floor(d.getMinutes()/15),
            stamp = h + ":" + (m === 0 ? "00" : m),
            pos = arr.indexOf(stamp);

        return arr.slice(pos).concat(arr.slice(0,pos));
    }
  }
}
</script>