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Here is a working another example https://jsfiddle.net/ffeohmk4/2/
getFinalList () {
return this.filteredOptions = this.options.filter(option => {
return option.value.toLowerCase().indexOf(this.searchValue.toLowerCase()) > -1;
})
}
<el-select v-model="searchValue" filterable placeholder="Select" :filter-method="setSearchInput">
<el-option v-for="item in getFinalList" :key="item.value" :label="item.label" :value="item.value">
</el-option>
Source:stackexchange.com