I am not aware of an OOTB feature to export the Most Popular Items search query to excel.
How may this be achieved?
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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.