Override the ListCompare block.

Create Vendor/Module/etc/di.xml on your custom module

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <preference for="MagentoCatalogBlockProductCompareListCompare" type="VendorModuleBlockProductCompareListCompare" />
</config>

Create Vendor/Module/Block/Product/Compare/ListCompare.php

<?php
namespace VendorModuleBlockProductCompare;

class ListCompare extends MagentoCatalogBlockProductCompareListCompare
{
	public function __construct(
        MagentoCatalogBlockProductContext $context,
        MagentoFrameworkUrlEncoderInterface $urlEncoder,
        MagentoCatalogModelResourceModelProductCompareItemCollectionFactory $itemCollectionFactory,
        MagentoCatalogModelProductVisibility $catalogProductVisibility,
        MagentoCustomerModelVisitor $customerVisitor,
        MagentoFrameworkAppHttpContext $httpContext,
        MagentoCustomerHelperSessionCurrentCustomer $currentCustomer,
        MagentoFrameworkObjectManagerInterface $objectManager,
        array $data = []
    ) {
    	$this->objectManager = $objectManager;
        parent::__construct($context,$urlEncoder,$itemCollectionFactory,$catalogProductVisibility,$customerVisitor,$httpContext,$currentCustomer,$data);
    }

	/**
     * Retrieve Product Compare items collection
     *
     * @return MagentoCatalogModelResourceModelProductCompareItemCollection
     */
    public function getItems()
    {
    	if ($this->_items === null) {
            $this->_compareProduct->setAllowUsedFlat(false);

            $this->_items = $this->_itemCollectionFactory->create();
            $this->_items->useProductItem(true)->setStoreId($this->_storeManager->getStore()->getId());

            if ($this->httpContext->getValue(MagentoCustomerModelContext::CONTEXT_AUTH)) {
                $this->_items->setCustomerId($this->currentCustomer->getCustomerId());
            } elseif ($this->_customerId) {
                $this->_items->setCustomerId($this->_customerId);
            } else {
            	/****** Custom Code ******/
                $sessionManager  = $this->objectManager->create('MagentoFrameworkSessionSessionManagerInterface');
                $visitor = $sessionManager->getVisitorData();
                if(!$this->_customerVisitor->getId() && isset($visitor['visitor_id'])){
                	$visitorid = $visitor['visitor_id'];
                }else{
                	$visitorid = $this->_customerVisitor->getId();
                }
            	/****** Custom Code ******/
                $this->_items->setVisitorId($visitorid);
            }

            $this->_items->addAttributeToSelect(
                $this->_catalogConfig->getProductAttributes()
            )->loadComparableAttributes()->addMinimalPrice()->addTaxPercents()->setVisibility(
                $this->_catalogProductVisibility->getVisibleInSiteIds()
            );
        }
        return $this->_items;
    }
}