The data is said to include information from networks as well as from individual computers and smart-phones.
Der Spiegel cites documents provided by US intelligence leaker Edward Snowden.
The former Central Intelligence Agency technical worker is the source of some of the biggest information leaks in US historychina virtual office.
A file photo taken on June 24, 2014 shows Edward Snowden speaking to European officials via videoconference at the Council of Europe in Strasbourg, eastern France. Edward Snowden has revealed huge US surveillance operations
A number of US allies, including Germany, have already expressed anger over Snowden-based spying allegations.
'Google Earth of the Internet'
The Spiegel article claims that the NSA ( National Security Agency) and the UK's GCHQ (Government Communications Headquarters) are able to eavesdrop on telecom companies such as Deutsche Telekom, Netcologne, Stellar and Cetel Sim
.
The Treasure Map programme, which the newspaper calls "the Google Earth of the Internet," is said to give the agencies access to data about the network structure and also through individual routers to subscribers' personal devices.
Der Spiegel warns that the information obtained could be used for planning sophisticated cyber-attacks.
The Treasure map was first mentioned last year by the New York Times, which says the programme collects Wifi network and geo-location data, as well as between 30 and 50 million unique internet provider addresses — information that can reveal the owner and location of a computer or mobile device.
Deutsche Telekom and Netcologne both told Der Spiegel they had not identified any evidence of manipulation or external access to their networks.
But Deutsche Telekom's IT security head Thomas Tschersich said: "The access of foreign secret services to our network would be totally unacceptable hair loss treatment
."