A delegation of German chancellery and intelligence officials reached the deal during talks at the White House this week, the Frankfurter Allgemeine Sonntagszeitung (FAS) reported in its edition.
The accord is set to be concluded early next year, it said, citing sources close to the German government.
Contacted by AFP, a government spokeswoman declined to comment.
Spy claims have been ricocheting across the Atlantic in a row that has frazzled ties between US and European allies.
Top German envoys were in Washington to rebuild a "basis of trust" after alleged US tapping of Chancellor Angela Merkel's phone in sweeping surveillance operations that have outraged Europe.
Merkel's spokesman said the talks were aimed at clarifying the allegations and working out "a new basis of trust and new regulation for our cooperation in this area".
The chancellor's foreign policy advisor Christoph Heusgen and intelligence coordinator Günter Heiss met top US officials including National Security Advisor Susan Rice, Director of National Intelligence James Clapper and counter-terrorism advisor Lisa Monaco.
According to the FAS report, the head of Germany's secret service is now to hold a top-level meeting with US intelligence chiefs in Washington.
The government spokeswoman did not confirm plans for the meeting.
France, Italy and Spain have also protested after media reports, based on leaks from US fugitive Edward Snowden, that Washington collected tens of millions of European telephone calls and online communications as part of anti-terror operations.