Germany received information this week that the US National Security Agency (NSA) had bugged Merkel's mobile phone, prompting Berlin to summon the US ambassador, a move unprecedented in post-war relations between the close allies.
The NSA denied that Obama had been informed about the operation by the NSA chief in 2010, as reported by the German newspaper. But the agency did not comment directly on whether Obama knew about the bugging of Merkel's phone.
Both the White House and the German government declined comment.
The Wall Street Journal reported on Sunday that the NSA ended the programme that involved Merkel after the operation was uncovered in an Obama administration review that began this summer. The NSA was not immediately available for comment on the report.
The programme also involved as many as 35 other world leaders, some of whom were still being monitored, according to the WSJ report, which was attributed to US officials.
Citing a source in Merkel's office, some German media have reported that Obama apologised 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 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.
The NSA said, however, that Alexander had never discussed any intelligence operations involving Merkel with Obama.
"[General] Alexander did not discuss with President Obama in 2010 an alleged foreign intelligence operation involving German Chancellor Merkel, nor has he ever discussed alleged operations involving Chancellor Merkel", NSA spokeswoman Vanee Vines said in an emailed statement.
"News reports claiming otherwise are not true."
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.
White House spokeswoman Caitlin Hayden declined to comment and reiterated the standard policy line that the United States gathers foreign intelligence of the type gathered by all nations.
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".
The NSA first eavesdropped on Merkel's predecessor Gerhard Schroeder after he refused to support President George W. Bush's war in Iraq and was extended when Merkel took over in 2005, the paper said.
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.
Breach of trust
Merkel has said she uses one mobile phone and that all state-related calls are made from encrypted lines.
The rift over US surveillance activities first emerged this year with reports that Washington had bugged European Union offices and tapped half a billion phone calls, emails and text messages in Germany in a typical month.
Merkel's government said in August - just weeks before a German election - that the United States had given sufficient assurances it was complying with German law.
This week's news has reignited criticism of the US surveillance. Volker Kauder, head of Merkel's party in parliament, called it a "grave breach of trust" and said the United States should drop its "global power demeanour".
Kauder said, however, that he was against halting negotiations on a European free trade agreement with the United States, a call made by Social Democrats and some of Merkel's Bavarian allies.
Interior Minister Hans-Peter Friedrich told Bild am Sonntag: "Bugging is a crime and those responsible for it must be held to account."
The Social Democrats, with whom Merkel is holding talks to form a new government, have joined calls from two smaller opposition parties for a parliamentary investigation into the US surveillance, but Kauder has rejected the idea.
SPD parliamentary whip Thomas Oppermann said former NSA contractor Edward Snowden, who leaked many of the sensitive documents, could be called as a witness. Snowden is living in Russia, out of reach of US attempts to arrest him.