The president, who is 74, has not been seen in public since travelling to the Mayo Clinic in Rochester, Minnesota on Aug. 2 for what his office described then as an operation on his left knee.
"Talabani received surgery on one of the blood vessels in his heart. It was a successful operation," Mustafa Sowrash, a senior official in Talabani's PUK party, told Reuters in the party's base, the Iraqi Kurdish city of Sulaimaniya.
"The physicians informed him that he may leave the hospital today or tomorrow, and he will go to Washington," he said. "His return to Iraq is not far off."
A Kurd, Talabani has been president since 2005. Although he does not wield executive power in Iraq, his role is seen as critical in maintaining the country's delicate ethnic balance.
He had a major impact on Iraqi politics last month when he vetoed a law allowing provincial elections. His fellow Kurds opposed the law because they feared it would have restricted their hope of controlling the oil-rich city of Kirkuk.
His two vice presidents are a Shi'ite and a Sunni Arab.
Reuters reported earlier on Thursday that several senior officials had said on condition they not be named that the surgery involved the president's heart.
Talabani's office said this week that his treatment had been a success, but would not confirm that it involved his heart.
Sowrash said Talabani was awaiting a decision as to whether he still needed an operation on his knee.
Talabani has had health problems in the past.
The Mayo Clinic confirmed he has been a patient but would give no further details.
"At the patient's request, we have no information," a spokeswoman for the clinic said.
