According to people with knowledge on the matter, the Federal Reserve Bank of New York - which is one of 12 regional Reserve Banks - wants to see more information from the lenders with regard to their day-to-day operation funds.
The group has been holding detailed discussions with the institutions in order to better understand their vulnerability to wider financial concerns.
Officials at the body said they were very concerned that European banks could encounter funding problems in the US, with regulators eager to stamp out the possibility of a recurrence of the 2008 financial crisis.
A number of Europe's biggest banks - including UniCredit SpA of Italy, Societe Generale SA from France and Germany's Deutsche Bank AG - are known to have major operations in the US.
By Asim Shah