The reports say the latest allegations came from documents provided by the fugitive US analyst Edward Snowden.
They say the NSA collected the numbers and locations of the caller and the recipient, but not the calls' content.
This comes as an EU parliamentary delegation is due to meet US officials in Washington to convey concerns.
The officials from the European parliament's Civil Liberties Committee will speak to members of Congress to gather information.
It is not clear how the alleged surveillance was carried out, whether it was from monitoring fibre-optic cables, data (including metadata) obtained from telecoms companies, or other means.