The Wall Street Journal says Obama knew US was monitoring Merkel as early as 2010, but failed to put stop to program.
The program also involved as many as 35 other world leaders, some of whom were still being monitored, according to the report, which was attributed to US officials.
In response to the WSJ report, National Security Council spokeswoman Caitlin Hayden noted in a statement that Obama had ordered a review of US surveillance capabilities.
"Through this review, led by the White House, the United States is reviewing the way that we gather intelligence to ensure that we properly account for the security concerns of our citizens and allies and the privacy concerns that all people share," Hayden said, adding that she was not in a position to discuss the details.
Citing a source in Merkel's office, some German media have reported that Obama apologized to Merkel when she called him on Wednesday, and told her that he would have stopped the bugging happening had he known about it.
But German newspaper of Bild am Sonntag, citing a "US intelligence worker involved in the NSA operation against Merkel", said NSA chief General Keith Alexander informed Obama in person about it in 2010.
"Obama didn't stop the operation back then but let it continue," the mass-market paper quoted the source as saying.
Bild am Sonntag said Obama in fact wanted more material on Merkel, and ordered the NSA to compile a "comprehensive dossier" on her. "Obama, according to the NSA man, did not trust Merkel and wanted to know everything about the German," the paper said.
Bild said the NSA had increased its surveillance, including the contents of Merkel's text messages and phone calls, on Obama's initiative and had started tapping a new, supposedly bug-proof mobile she acquired this summer, a sign the spying continued into the "recent past".
Eighteen NSA staff working in the US embassy, some 800 metres (yards) from Merkel's office, sent their findings straight to the White House, rather than to NSA headquarters, the paper said. Only Merkel's encrypted landline in her office in the Chancellery had not been tapped, it added.
Bild said some NSA officials were becoming annoyed with the White House for creating the impression that US spies had gone beyond what they had been ordered to do.
NJF/NJF