Good for Gold news the metal German newspaper Bild am Sonntag, citing a "US intelligence worker involved in the NSA operation against Merkel", said Mr Alexander informed Mr Obama in person about it in 2010.
"Obama didn't stop the operation back then but let it continue," the paper quoted the source as saying.
Bild am Sonntag said Mr Obama in fact wanted more material on Ms 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.
The paper said the NSA had increased its surveillance, including the contents of Ms Merkel's text messages and phone calls, on Mr 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".
The NSA first eavesdropped on Ms Merkel's predecessor Gerhard Schroeder after he refused to back then-president George W Bush's war in Iraq and continued when Ms Merkel took over in 2005, the paper said.
Eighteen NSA staff working in the US embassy, some 800 metres from Ms Merkel's office, sent their findings straight to the White House, rather than to NSA headquarters!