If you are using prestashop classic theme you can do it like this:
Open file YOUR_STORE_NAME/themes/classic/templates/catalog/_partials/productlist.tpl
Change this:
<div class="products{if !empty($cssClass)} {$cssClass}{/if}" itemscope itemtype="http://schema.org/ItemList"> {foreach from=$products item="product" key="position"} {include file="catalog/_partials/miniatures/product.tpl" product=$product position=$position} {/foreach} </div>
To this:
<div class="products{if !empty($cssClass)} {$cssClass}{/if}" itemscope itemtype="http://schema.org/ItemList"> {foreach from=$products item="product" key="position"} {if $product.quantity > 0 && $page.page_name == "prices-drop"} {* crezzur.com: add check if product has quantity, if not do not display product *} {include file="catalog/_partials/miniatures/product.tpl" product=$product position=$position} {else} {include file="catalog/_partials/miniatures/product.tpl" product=$product position=$position} {/if} {/foreach} </div>
Now only products with stock will be displayed.