According to the newspaper, the letter asked Google whether it had "fulfilled all the necessary requirements" on data protection.
Stored data by Google includes the search item, internet server address and sometimes details on cookies or identifier programs.
The EU is concerned that such data could be used to identify individuals and create profiles based on political stance, religion or sexuality.
In March, Google cut its storage time of such data from an indefinite period to two years in an attempt to allay such fears.
No-one from the European Commission was immediately available for comment.