A White House spokesman said he could not comment directly but efforts were being made to solve the problem.
Earlier, German Chancellor Angela Merkel voiced her concerns about the alleged US spy in German intelligence, while on a visit to China.
"It would be a clear contradiction of what I consider to be trusting co-operation" with the US, she said.
She said that if the allegations about a double agent were true, it would constitute a serious breach of trust.
"If the reports are correct, it would be a serious case," Ms Merkel said on Monday while at a news conference with Chinese Premier Li Keqiang.
It is the second day of her three-day visit, which is dominated by trade issues.
The latest twist in the ongoing spying row between the two countries happened last week when a German employee of the country's foreign intelligence service (BND) was arrested.
The man is suspected of having handed over more than 200 documents over a two-year period in exchange for 25,000 euros (£20,000; $34,000).
Questioned by reporters on Monday, White House spokesman Josh Earnest praised the "valuable" relationship the US had with Germany and said: "We are going to work with the Germans to resolve this situation appropriately,"
Analysis - Stephen Evans, BBC News, Berlin
Spying is particularly sensitive in Germany, whether it's listening in to Chancellor Merkel's phone or reading secret documents meant for a parliamentary committee. Mrs Merkel grew up in East Germany where the intrusions of the secret police - the Stasi - were pervasive and poisonous. And democracy has something of a sacred quality in Germany today because of the Nazi and then the Communist years.
"Outrage" runs across the political spectrum - it's not just a "chattering class" issue. Wolfgang Bosbach, for example, who is the Christian Democrat [centre-right] head of the Bundestag committee which oversees interior affairs, questioned whether the US and Germany could be considered as "partners" any more.
The first allegation of spying came just after President Obama's visit to Berlin where he was greeted as a long-lost friend. And this latest one concerns material for the very parliamentary committee set up to investigate the previous allegation. Spies spy, and no doubt spies spy on friends, but there are political consequences when they are caught at it, even if it's just in terms of a loss of goodwill.
German-US relations have been strained since it emerged that the US National Security Agency (NSA) had been monitoring Ms Merkel's mobile phone calls.
The scale of NSA surveillance was revealed by US whistleblower Edward Snowden, a former NSA contractor who remains a fugitive in Russia.