Default variation not selected in the cross-sells pop-up

Hello,
We have set up the cross sell pop-up for one of our products.
This product is of variable type and has a default variation.
When the product page is displayed, the default value is correctly displayed in the variations selector.
But in the pop-up, the default value is not selected under the product.
Could you help me to display the default value in the popup selector ?
Thank you in advance