Please follow below steps to add drop-down option in admin grid filter :

Step 1:  Below is my module file path.

File Path is : NikGridfilterBlockAdminhtmlGrid.php

protected function _prepareColumns() {
 $this->addColumn(
 'mobile_type', [
 'header' => __('Status'),
 'index' => 'status',
 'width' => '50px',
 'type' => 'options',
 'options' => Status::getAvailableStatus(), //get dropdown result
 ] );
 }

Step : 2  Below is my render class which will convert a numeric value to string value (You can Modify as per your requirements)

File path is: NikGridfilterBlockAdminhtmlRendererStatus.php

<?php
 namespace NikGridfilterBlockAdminhtmlRenderer;
class Status extends MagentoBackendBlockWidgetGridColumnRendererAbstractRenderer
 {
protected $_storeManager;
public function __construct(
 MagentoBackendBlockContext $context,
 MagentoStoreModelStoreManagerInterface $storeManager,
 array $data = []
 ) {
 parent::__construct($context, $data);
 $this->_storeManager = $storeManager;
 }
public function render(MagentoFrameworkDataObject $row) {
 return [
 array("1" => "Status-Yes" , "2" => "Status-No")
 ]
 }
 }