Spiegel said that the BND planned a 100 million euro ($130 million) programme over the next five years to expand web monitoring with up to 100 new staff members on a "technical reconnaissance" team.
The report came ahead of a state visit to Berlin by US President Barack Obama during which the German government has pledged to take up the controversy over the US phone and Internet surveillance programmes.
Spiegel said the BND aimed to monitor international data traffic "as closely as possible", noting that it currently kept tabs on about five percent of emails, Internet calls and online chats while German law allowed up to 20 percent.

Unlike the US National Security Agency (NSA), Germany's BND is not allowed to store the data but must filter it immediately.
"Of course our intelligence services must have an Internet presence," Interior Minister Hans-Peter Friedrich told Der Spiegel, without confirming the details of the report.
The state must ensure "that we balance the loss of control over communication by criminals with new legal and technological means," he added.
Under the so-called PRISM programme that was exposed this month, the NSA can issue directives to Internet firms such as Google and Facebook to gain access to emails, online chats, pictures, files and videos uploaded by foreign users.
Germany, where sensitivity over government surveillance is particularly heightened due to widespread spying on citizens by communist East Germany's despised Stasi, said last week it was sending a list of questions to the Obama administration about the programme.
The European Union has also expressed disquiet over the scheme and warned of "grave adverse consequences" to the rights of European citizens.

AFP