Bild am Sonntag newspaper quoted US intelligence sources as saying that National Security Agency chief Keith Alexander had briefed Obama on the operation against Merkel in 2010.
"Obama did not halt the operation but rather let it continue," the newspaper quoted a high-ranking NSA official as saying.
Meanwhile newsweekly Der Spiegel reported ahead of its Monday issue that leaked NSA documents showed Merkel's phone had appeared on a list of spying targets since 2002, and was still under surveillance weeks before Obama visited Berlin in June.
The spying row has prompted European leaders to demand a new deal with Washington on
intelligence gathering that would maintain an essential alliance while keeping the fight against terrorism on track.
Germany will send its own spy chiefs to the United States next week to demand answers following the allegations that US intelligence has been tapping Merkel's mobile phone, as the row threatened to fray transatlantic ties.
Merkel confronted Obama with the suspicion in a phone call on Wednesday saying that spying on allies would be a "breach of trust" between international partners.
The charges also prompted Berlin to summon the US ambassador -- a highly unusual move between the close allies.
The Frankfurter Allgemeine Sonntagszeitung reported Saturday that Obama had told Merkel during their call that he had been unaware of any spying against her. It did not cite its sources.
Der Spiegel said he had told her that if he had been informed of the operation he would have stopped it at once.
Other media reports said that Obama's National Security Advisor Susan Rice had also told German officials the president knew nothing of the spying.