Maliki said Iraq is prepared to facilitate the negotiations, The New York Times reported.
State Department officials declined to comment on Maliki's comments or what the United States may have done in response.
"Iraq is a partner of the United States and we are in regular conversations with Iraqi officials about a full range of issues of mutual interest, including Iran," Patrick Ventrell, a State Department spokesman, said. "As we have repeatedly said, we are open to direct talks with Iran in order to resolve the international community's concerns about Iran's nuclear program."
Maliki said he was relaying a message from Iranian officials. He said Iran's incoming president, Hassan Rouhani would be serious about any discussions with the United States.
Maliki did not disclose the names of any Iranian officials.
The Times said some Western officials are unsure if the Iranians chose Iraq as a messenger, or if the idea was Maliki's.