US, Iranian and Iraqi officials could not confirm the report.
According to Sharqiya, Talabani told Iraqi and Arab writers during a spring cultural festival that the talks took place in the lakeside mountain resort of Dukan and that discussions were ''dedicated to the Iraqi issue''.
It said Talabani, a Kurd, expected such meetings to continue to be held, but provided no more details.
Iranian and US officials have said in the past that they would hold talks to discuss Iraq, without giving a date.
A spokesman at the US embassy in Baghdad said he was unaware of such a meeting. A spokesman at Talabani's office also said he knew nothing about the reported talks in Dukan, where Talabani frequently holds political meetings. Talabani was not immediately available for comment.
There was no immediate comment from Tehran.
The United States accuses Iran of fuelling sectarian violence in Iraq, a charge dismissed by Tehran, which says the presence of US troops is to blame.
Both sides had said any such talks would only cover Iraq, although some analysts said it could open a conduit for discussion of other issues, particularly the dispute over Iran's nuclear programme.
Iran and Iraq fought a war from 1980-88 and, until Saddam Hussein was toppled by the US invasion in 2003, had a frosty relationship.
REUTERS PG RN2018