I am not aware of an OOTB feature to export the Most Popular Items search query to excel.
How may this be achieved?
Per my knowledge you may need to do it manually with PowerShell.
In Microsoft.Office.Server.Search.Analytics namespace, there is a method “UsageAnalytics.GetAnalyticsItemData” which can help to “Retrieves aggregated usage data for a specified item for a specified event type”.
You may use it as a start point.