Short answer
Carefully consider to file a report with the Internet Crime Complaint Center (www.ic3.gov), a partnership between the Federal Bureau of Investigation and the National White Collar Crime Center.
Long answer
The following quote, from https://support.google.com/mail/answer/190735?hl=en, is regarding impersonation, but this also could apply to other suspicious activities that could lead to commit cybercrimes
Impersonation
If you believe someone has created a Gmail address in an attempt to
impersonate your identity, you may wish to file a report with the
Internet Crime Complaint Center (www.ic3.gov), a partnership between
the Federal Bureau of Investigation and the National White Collar
Crime Center.
In addition, we recommend contacting your state's Office of Consumer
Protection.
Gmail is unable to participate in mediations involving third parties
regarding impersonation. To read the Gmail Terms of Use, please visit:
https://www.gmail.com/intl/en/mail/help/terms.html.
From www.ic3.gov
Filing a Complaint with the IC3
The IC3 accepts online Internet crime complaints from either the
actual victim or from a third party to the complainant. We can best
process your complaint if we receive accurate and complete information
from you. Therefore, we request that you provide the following
information when filing a complaint:
- Your name
- Your mailing address
- Your telephone number
The name, address, telephone number, and Web address, if available, of
the individual or organization you believe defrauded you. Specific
details on how, why, and when you believe you were defrauded. Any
other relevant information you believe is necessary to support your
complaint.